mixed and galerkin finite element approximation of flow in a linear viscoelastic porous medium we propose two fully discrete mixed and galerkin finite element approximations to a system of equations describing the slow flow of a slightly compressible single phase fluid in a viscoelastic porous medium one of our schemes is the natural one for the backward euler time discretization but due to the viscoelasticity seems to be stable only for small enough time steps the other scheme contains a lagged term in the viscous stress and pressure evolution equations and this is enough to prove unconditional stability for this lagged scheme we prove an optimal order a priori error estimate under ideal regularity assumptions and demonstrate the convergence rates by using a model problem with a manufactured solution the model and numerical scheme that we present are a natural extension to poroviscoelasticity of the poroelasticity equations and scheme studied by philips and wheeler in for example philip joseph philips mary f wheeler comput geosci 11 2007 145 158 although importantly their algorithms and codes would need only minor modifications in order to include the viscous effects the equations and algorithms presented here have application to oil reservoir simulations and also to the condition of hydrocephalus water on the brain an illustrative example is given demonstrating that even small viscoelastic effects can produce noticeable differences in long time response to the best of our knowledge this is the first time a mixed and galerkin scheme has been analysed and implemented for viscoelastic porous media

the yang lee edge singularity in spin models on connected and non connected rings renormalization group arguments based on a 3 field theory lead us to expect a certain universal behavior for the density of partition function zeros in spin models with short range interaction such universality has been tested analytically and numerically in different d 1 and higher dimensional spin models in d 1 one finds usually the critical exponent 1 2 recently we have shown in the d 1 blume emery griffiths beg model on a periodic static lattice one ring that a new critical behavior with 2 3 can arise if we have a triple degeneracy of the transfer matrix eigenvalues here we define the d 1 beg model on a dynamic lattice consisting of connected and non connected rings non periodic lattice and check numerically that also in this case we have mostly 1 2 while the new value 2 3 can arise under the same conditions of the static lattice triple degeneracy which is a strong check of universality of the new value of we also show that although such conditions are necessary they are not sufficient to guarantee the new critical behavior

renormalisation group recursions by mean field approximations within a renormalisation group strategy different rescaled mean field approximations for the magnetisation are combined good qualitative estimates are obtained for the critical properties of classical and quantum spin systems a particularly simple realisation of the method yields recursions for arbitrary dimensionality d the critical couplings are accurate for all d and have the correct asymptotic behaviour for d approaching infinity

a mean field renormalisation group approach to ising and q 3 state potts models with long range interactions in one dimension abstract we study the one dimensional potts model with long range interactions decaying with distance r as r 1 an extended mean field renormalisation group procedure is applied such that three finite size linear lattices are compared in order to evaluate critical temperatures and exponents for the q 2 ising model and q 3 such that the transition is a continuous one cases good results are obtained whenever comparison with exact results or with other procedures is possible moreover we evaluate the surface field exponent for these models we have been able to go to rather large lattices and then a suitable finite size scaling procedure is employed to obtain the results in the thermodynamic limit

parafermions and surface exponents of self dual z n spin models from conformal invariance the author studies the critical behaviour of a family of self dual two dimensional spin models with z n symmetry n or 8 in its hamiltonian formulation using the relations between the mass gap amplitudes of the hamiltonian in a finite strip and the critical exponents he estimates the anomalous dimensions of the parafermions occurring in the underlying field theory as well as the surface exponents

the folk theorem for games with private almost perfect monitoring we prove the folk theorem for discounted repeated games under private almost perfect monitoring our result covers all finite n player games that satisfy the usual full dimensionality condition mixed strategies are allowed in determining the individually rational payoffs we assume no cheap talk communication between players and no public randomization device

on a conjecture of alley and alder for fluids and lorentz models we discuss a conjecture of alley and alder predicting a relation between the four point and the two point velocity autocorrelation functions for fluids and lorentz models at sufficiently long times if the conjecture is correct a modified burnett coefficient can be defined which has a finite value contrary to the ordinary burnett coefficient which is divergent the conjecture is tested for four classes of models with different methods for three dimensional fluids mode coupling theory yields a negative result the conjecture is confirmed for thed dimensional deterministic lorentz gas d 2 and for a class ofd dimensional stochastic lorentz models d 1 by low density kinetic theory as well as by rigorous results available for one dimension for yet another class of one dimensional stochastic lorentz models which are exactly solvable in one dimension the result is negative again all four classes of models show long time tails in the velocity autocorrelation function and have a finite diffusion coefficient

constitutive model of brain tissue suitable for finite element analysis of surgical procedures realistic finite element modelling and simulation of neurosurgical procedures present a formidable challenge appropriate finite deformation constitutive model of brain tissue is a prerequisite for such development in this paper a large deformation linear viscoelastic model suitable for direct use with commercially available finite element software packages such as abaqus is constructed the proposed constitutive equation is of polynomial form with time dependent coefficients the model requires four material constants to be identified the material constants were evaluated based on unconfined compression experiment results the analytical as well as numerical solutions to the unconfined compression problem are presented the agreement between the proposed theoretical model and the experiment is good for compression levels reaching 30 and for loading velocities varying over five orders of magnitude the numerical solution using the finite element method matched the analytical solution very closely

finite lattice extrapolations for z3 and zs models a method is presented to accelerate the convergence of finite lattice sequences to their bulk limit the calculation of highly accurate estimates of the critical parameters of the bulk system is then possible applied to the hamiltonian version of the z3 model three state potts model in 1 1 dimensions these techniques yield estimates for the exponents gamma 1 444 or 0 0001 nu 0 8333 or 0 0003 and alpha 0 33 or 0 01 for the z5 model the presence of a kosterlitz thouless transition is confirmed

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

multicanonical monte carlo simulations canonical monte carlo simulations of disordered systems like spin glasses and systems undergoing first order phase transitions are severely hampered by rare event states which lead to exponentially diverging autocorrelation times with increasing system size and hence to exponentially large statistical errors one possibility to overcome this problem is the multicanonical reweighting method using standard local update algorithms it could be demonstrated that the dependence of autocorrelation times on the system size v is well described by a less divergent power law v with 1 3 depending on the system after a brief review of the basic ideas combinations of multicanonical reweighting with non local update algorithms will be discussed with the multibondic algorithm which combines multicanonical reweighting with cluster updates the dynamical exponent can be reduced to unity the optimal value one would expect from a random walk argument asymptotically for large system sizes the multibondic algorithm therefore always performs better than the standard multicanonical method finally it is shown that a combination with multigrid update techniques improves the performance of multicanonical simulations by roughly one order of magnitude uniformly for all system sizes

discontinuity of the magnetization in one dimensional 1 x y 2 ising and potts models results from percolation theory are used to study phase transitions in one dimensional ising and q state potts models with couplings of the asymptotic form j sub x y approx const absolute value x y sup 2 for translation invariant systems with well defined lim sub x infinity x sup 2 j sub x j sup possibly o or infinity we establish 1 there is no long range order at inverse temperatures beta with beta j sup less than or equal to1 2 if beta j sup q then by sufficiently increasing j sub 1 the spontaneous magnetization m is made positive 3 in models with 0 j sup infinity the magnetization is discontinuous at the transition point as originally predicted by thouless and obeys m beta sub c less than or equal to 1 beta sub c j sup sup 1 2 4 for ising q 2 models with j sup infinity it is noted that the correlation function decays as beta approx c beta absolute value x y sup 2 whenever beta beta sub c points 1 3 are deduced from previous percolation results by utilizing the fortuin kasteleyn representation which also yields other results of independent interest relating potts models with different values of q

the 2 1 d ising model on a triangular lattice the 2 1 d ising model on a triangular lattice is explored for lattices of up to 5 5 sites finite size scaling techniques are used to estimate the critical parameters xc 0 2096 2 nu 0 627 4 beta 0 322 6 gamma 1 236 8 these agree with previous estimates within errors and with the hypotheses of universality and hyperscaling the behaviour at low temperatures is also studied and theoretical predictions of finite size scaling at a first order transition are confirmed

one dimensional models with 1 r2 interactions the critical behaviour of a general discrete one dimensional model with inverse square interactions is discussed using renormalisation group methods

first order transition in the one dimensional three state potts model with long range interactions the first order phase transition in the three state potts model with long range interactions decaying as 1 r 1 ensuremath sigma has been examined by numerical simulations using the recently proposed luijten bl ote algorithm by applying scaling arguments to the interface free energy the binder s fourth order cumulant and the specific heat maximum the change in the character of the transition through variation of parameter ensuremath sigma was studied

first order transitions for n vector models in two and more dimensions rigorous proof we prove that various so n invariant n vector models with interactions which have a deep and narrow enough minimum have a first order transition in the temperature the result holds in dimensions two or more and is independent of the nature of the low temperature phase

empirical distributions of beliefs under imperfect observation let xn n be a process with values in a finite set x and law p and let yn f xn be a function of the process at stage n the conditional distribution pn p xnx1 xn1 element of x is the belief that a perfect observer who observes the process online holds on its realization at stage n a statistician observing the signals y1 yn holds a belief enp pnx1 xn on the possible predictions of the perfect observer given x and f we characterize the set of limits of expected empirical distributions of the process en when p ranges over all possible laws of xn n

the critical behaviour of the long range potts chain from the largest cluster probability distribution abstract we present the numerical study of the one dimensional potts model with power law decaying ferromagnetic interactions the largest cluster probability distribution is obtained by monte carlo simulations using the swendsen wang cluster algorithm with cumulative probabilities the finite size scaling analysis of the largest cluster is used to derive the critical behaviour in the non classical regime of this model for various values of q

finite size scaling and universality in the 2 1 d ising model the energy and magnetisation density of the 2 1 d ising model are investigated for the thermal exponent the author finds xepsilon 1 42 or 0 02 in agreement with hyperscaling the privman fisher universality hypothesis is confirmed by two methods first the author presents at the critical point numerical data for the finite size scaling amplitudes of the singular free energy magnetisation susceptibility and surface tension and checks them for universality second using the explicitly computed eigenvectors of the hamiltonian it is shown that the ratios of matrix elements of the energy and magnetisation density are universal

tsallis scaling and the long range ising chain a transfer matrix approach a numerically efficient transfer matrix tm approach is introduced to investigate the long range ising spin chain results obtained within this procedure are primarily used to verify the tsallis scaling hypothesis for long range systems with an ensuremath alpha power law decay of the interaction constants both in the extensive ensuremath alpha g1 and nonextensive ensuremath alpha l1 regimes results for finite size systems taking into account all interactions between spins up to 24 sites apart show that the conjecture is satisfied with a very good precision less than 0 004 for all temperature intervals this tm procedure is further used to investigate several other thermodynamic and critical properties of this system and it may also be extended to similar one dimensional long range systems

continuously varying exponents and the value of the central charge the author shows that the conformal field theories describing two dimensional critical behaviour with continuously varying exponents must have central charge c 1 if a there are no conserved spin 2 currents other than the stress tensor and b the marginal operator responsible for the line of fixed points does not mix with other operators in such cases one may show the existence of a fixed line knowing only the four point function of the marginal operator the author applies this to the ashkin teller model and the xy model with fourfold symmetry breaking

differential versus integral formulation of fractional hyperviscoelastic constitutive laws for brain tissue modelling for years interest has been constantly growing in biological tissue modelling particularly the mechanical study of the brain has become a major topic in the field of biomechanics a global model of this organ including a realistic mesh and suitable constitutive laws for the different tissues would find applications in various domains such as neurosurgery haptic device design or car manufacturing to evaluate the possible trauma due to an impact several constitutive models have already been designed regarding the strong strain rate dependence of the stress strain curves available in the literature we decided to describe brain tissue as a viscoelastic medium through the use of the fractional derivation operator thanks to this approach we can derive a convolution based model with the mittag leffler function as the regularized kernel

phase diagram of a stochastic cellular automaton with long range interactions abstract a stochastic one dimensional cellular automaton with long range spatial interactions is introduced in this model the state probability of a given site at time t depends on the state of all the other sites at time t 1 through a power law of the type 1 r r being the distance between sites for this model reduces to the domany kinzel cellular automaton the dynamical phase diagram is analyzed using monte carlo simulations for 0 we found the existence of two different regimes one for 0 1 and the other for 1 it is shown that in the first regime the phase diagram becomes independent of regarding the frozen active phase transition in this regime a strong evidence is found that the mean field prediction for this model becomes exact a result already encountered in magnetic systems it is also shown that for replicas evolving under the same noise the long range interactions fully suppress the spreading of damage for 0 1

long range one dimensional potts models a cluster mean field and extrapolation approach we obtain approximations for the critical temperature tc of q state ferromagnetic potts models on one dimensional lattices with algebraically decaying ferromagnetic pair interactions i e decaying as 1 r with 1 2 initially we use a cluster mean field method to get approximations to the critical temperature and we look at increasingly large clusters this gives us a sequence of ever more accurate approximate values which can be used as input to various extrapolation algorithms we see that as the interaction decreases more slowly and the value of q increases we obtain more and more accurate tc estimates our best estimates we believe to be correct to four figure accuracy

finite range scaling study of the 1d long range ising model the critical behaviour of the one dimensional ising model with long range ferromagnetic interactions decaying with distance r as 1 r1 sigma has been studied by scaling the range of interactions exact calculations have been done for a system with finite ranges up to the tenth neighbour for 0 sigma or 1 applying the range scaling the critical temperature critical exponent nu and the anomalous dimension of the order parameter have been calculated additional analysis of the convergence of the method has been performed by applying the vanden broeck and schwartz extrapolation procedure in addition to the simple least squares approximation and by evaluating the convergence exponents

on the complexity of coordination many results on repeated games played by finite automata rely on the complexity of the exact implementation of a coordinated play of length n for a large proportion of sequences this complexity appears to be no less than n we study the complexity of a coordinated play when allowing for a few mismatches we prove the existence of a constant c such that if m ln m n c for almost any sequence of length n there exists an automaton of size m that achieves a coordination ratio close to 1 with it moreover we show that one can take any constant c such that c e x ln x where x is the size of the alphabet from which the sequence is drawn our result contrasts with neyman 1997 that shows that when m ln m n is close to 0 for almost no sequence of length n there exists an automaton of size m that achieves a coordination ratio significantly larger 1 x with it

a uniform tauberian theorem in dynamic programming we prove that in dynamic programming framework uniform convergence of v implies uniform convergence of vn and vice versa moreover both have the same limit

yang lee zeros of triangular ising antiferromagnets abstract in our previous research by combining both the exact enumeration method microcanonical transfer matrix for a small system l 9 with the wang landau monte carlo algorithm for large systems to l 30 we obtained the exact and approximate densities of states g m e as a function of the magnetization m and exchange energy e for a triangular lattice ising model in this paper based on the density of states g m e the precise distribution of the yang lee zeros of triangular lattice ising antiferromagnets is obtained in a uniform magnetic field as a function of temperature a e 2 for a 9 9 lattice system also the feasibility of the yang lee zero approach combined with the wang landau algorithm is demonstrated as a result we obtained the magnetic exponents for triangular ising antiferromagnets at various temperatures

the one dimensional potts model with long range interactions a renormalization group approach the one dimensional q state potts model with ferromagnetic pair interactions which decay with the distance r as is considered we calculate through a real space renormalization group technique using kadanoff blocks of length b the critical temperature and the correlation length critical exponent as a function of for different values of q some of the very few known rigorous results for general q are reproduced by our approach several asymptotic behaviours are derived analytically for q 2 3 in the limit we also obtain extrapolated critical temperatures for arbitrary values of and for q 2 3 4 which we believe approximate the exact ones well except in the region near furthermore the use of another extrapolation procedure suitable only in the vicinity of led us to conjecture that the exact critical temperature is the same for any value of q we also verify that which is consistent with a recent conjecture of tsallis

informationally optimal correlation this papers studies an optimization problem under entropy constraints arising from repeated games with signals we provide general properties of solutions and a full characterization of optimal solutions for 2 2 sets of actions as an application we compute the minmax values of some repeated games with signals

fast flat histogram method for generalized spin models we present a monte carlo method that efficiently computes the density of states for spin models having any number of interaction per spin by combining a random walk in the energy space with collective updates controlled by the microcanonical temperature our method yields dynamic exponents close to their ideal random walk values reduced equilibrium times and very low statistical error in the density of states the method can host any density of states estimation scheme including the wang landau algorithm and the transition matrix method our approach proves remarkably powerful in the numerical study of models governed by long range interactions where it is shown to reduce the algorithm complexity to that of a short range model with the same number of spins we apply the method to the q state potts chains 3 ensuremath leqslant q ensuremath leqslant 12 with power law decaying interactions in their first order regime we find that conventional local update algorithms are outperformed already for sizes above a few hundred spins by considering chains containing up to 2 16 spins which we simulated in fairly reasonable time we obtain estimates of transition temperatures correct to five figure accuracy finally we propose several efficient schemes aimed at estimating the microcanonical temperature

the ising model with long range ferromagnetic interactions a variational method based on the nearest neighbour ising model is used to derive an expression for the low temperature correlation function in the ising model with long range ferromagnetic interactions also by expanding the correlation function directly the authors demonstrate that the characteristic power law behaviour at large distances is irrelevant in the critical region when above the marginal range of interaction

critical behaviour of the 1d q state potts model with long range interactions the critical behaviour of the one dimensional q state potts model with long range interactions decaying with distance r as r 1 sigma has been studied in the wide range of parameters 0 sigma or 1 and 1 16 or q or 64 a transfer matrix has been constructed for a truncated range of interactions for integer and continuous q and finite range scaling has been applied results for the phase diagram and the correlation length critical exponent are presented

operator content of the three state potts quantum chain the authors compute the lowest excitations of the spectra of the three state potts quantum chain with periodic and twisted boundary conditions these spectra can be understood in terms of eighteen irreducible representations of the virasoro algebra with c 4 5

optimized energy calculation in lattice systems with long range interactions we discuss an efficient approach to the calculation of the internal energy in numerical simulations of spin systems with long range interactions although since the introduction of the luijten blote algorithm monte carlo simulations of these systems no longer pose a fundamental problem the energy calculation is still an o n 2 problem for systems of size n we show how this can be reduced to an o n log n problem with a break even point that is already reached for very small systems this allows the study of a variety of until now hardly accessible physical aspects of these systems in particular we combine the optimized energy calcula tion with histogram interpolation methods to investigate the specific heat of the ising model and the first order regime of the three state potts model with long range interactions

finite lattice extrapolation algorithms two algorithms for sequence extrapolation due to van den broeck and schwartz 1979 and bulirsch and stoer 1964 are reviewed and critically compared applications to three state and six state quantum chains and to the 2 1 d ising model show that the algorithm of bulirsch and stoer is superior in particular if only very few finite lattice data are available

effective dimensions in networks with long range connections abstract one and two dimensional lattices of points are connected with long range links whose lengths are distributed according to p r r by changing the decay exponent one can go from d dimensional short range networks to dimensional networks topologically similar to random graphs an effective dimension d chem can be defined in terms of the shortest path properties of these networks these effective dimensions d chem are calculated here in one and two dimensions for system sizes of up to 10 7 points

reexamination of the long range potts model a multicanonical approach we investigate the critical behavior of the one dimensional q state potts model with long range lr interaction 1 r d sigma using a multicanonical algorithm the recursion scheme initially proposed by berg is improved so as to make it suitable for a large class of lr models with unequally spaced energy levels the choice of an efficient predictor and a reliable convergence criterion is discussed we obtain transition temperatures in the first order regime which are in far better agreement with mean field predictions than in previous monte carlo studies by relying on the location of spinodal points and resorting to scaling arguments we determine the threshold value sigma c q separating the first and second order regimes to two digit precision within the range 3 leq q leq 9 we offer convincing numerical evidence supporting sigma c q 1 0 for all q by virtue of an unusual finite size effect namely finite size scaling predicts a continuous transition in the thermodynamic limit despite the first order nature of the transition at finite size a qualitative account in terms of correlation lengths is provided finally we find the crossover between the lr and short range regimes to occur inside a narrow window 1 0 sigma 1 2 thus lending strong support to sak s scenario

new monte carlo algorithm entropic sampling we present a new monte carlo sampling algorithm with which one can obtain any desired distribution of the sampling in one monte carlo simulation the free energy and the entropy of a system can thus be obtained from a simple exercise of this algorithm the main idea is to sample directly the entropy of a system at infinite temperature importance sampling is shown to be a particular case of the new algorithm the algorithm is tested against the exact partition function of the ital l 4 simple cubic ising model a comparison with the multicanonical ensemble for the ital l 12 ital q 10 potts model shows that the new algorithm is more general and more efficient

finitely repeated games with finite automata the paper studies the implications of bounding the complexity of the strategies players may select on the set of equilibrium payoffs in repeated games the complexity of a strategy is measured by the size of the minimal automation that can implement it a finite automation has a finite number of states and an initial state it prescribes the action to be taken as a function of the current state and a transition function changing the state of the automaton as a function of its current state and the present actions of the other players the size of an automaton is its number of states the main results imply in particular that in two person repeated games the set of equilibrium payoffs of a sequence of such games g n n 1 2 converges as n goes to infinity to the individual rational and feasible payoffs of the one shot game whenever the bound on one of the two automata sizes is polynomial or subexponential in n and both the length of the game and the bounds of the automata sizes are at least n a special case of such result justifies cooperation in the finitely repeated prisoner s dilemma without departure from strict utility maximization or complete information but under the assumption that there are bounds possibly very large to the complexity of the strategies that the players may use

conformal structure in the spectrum of an altered quantum ising chain the ising model with an infinite line of defects is mapped onto a strip with two defect lines the hamiltonian spectrum is studied at the bulk critical point its exact diagonal form is found for an infinite number of sites the spectrum of physical excitations contains an infinite number of primary fields while the leading ground state energy correction is independent of the defect strength a novel algebraic structure interpolating between those belonging to periodic and free boundary conditions is signalled

finite size scaling in the 2 1 d ising model hamiltonian eigenvalues are calculated for the 2 1 d ising model on lattices up to 5 5 sites finite size scaling techniques are used to estimate the critical coupling xc 0 329 or 0 001 and index v 0 635 or 0 005 the prospects are discussed for further applications of these methods in three and four dimensions

conformal invariance and correction to finite size scaling applications to the three state potts model corrections to finite size scaling are determined numerically for several levels of the three state potts quantum chain with various boundary conditions it is found that the leading correction term behaves like wo in the case of periodic and twisted boundary conditions the coefficients of the n o term are determined by the three point correlation functions of the conformal theory

correlated equilibria in two player repeated games with nonobservable actions four kinds of correlated equilibrium payoff sets in undiscounted repeated games with nonobservable actions are studied three of them the upper the uniform and banach lead to the same payoff set whereas the lower one in general is associated with a larger set the extensive form correlated equilibrium is also explored it turns out that both the regular and extensive form correlated equilibria yield the same sets of payoffs

the critical behaviour of self dual z n spin systems finite size scaling and conformal invariance this paper is concerned with the critical properties of a family of self dual two dimensional z n models whose bulk free energy is exactly known at the self dual point the author s analysis is performed by studying the finite size behaviour of the corresponding one dimensional quantum hamiltonians which also possess an exact solution at their self dual point by exploring finite size scaling ideas and the conformal invariance of the critical infinite system the author calculates for n up to 8 the critical temperature and critical exponents as well as the central charge associated with the underlying conformal algebra the results strongly suggest that the z n quantum field theory of zamolodchikov and fateev is the underlying field theory associated with these statistical mechanical systems the author also tests for the z 5 case the conjecture that these models correspond to the bifurcation points in the phase diagram of the general z n spin model where a massless phase originates

crossover from extensive to nonextensive behavior driven by long range d 1 bond percolation abstract we present a monte carlo study of a linear chain d 1 with long range bonds whose occupancy probabilities are given by p ij p r ij 0 p 1 0 where rij 1 2 is the distance between sites the 0 corresponds to the first neighbor mean field particular case we exhibit that the order parameter p equals unity p 0 for 0 1 presents a familiar behavior i e 0 for p pc and finite otherwise for 1 2 our results confirm recent conjecture namely that the nonextensive region 0 1 can be meaningfully unfolded as well as unified with the extensive region 1 by exhibiting p as a function of p where 1 p 1 p n n n 1 d 1 1 d n being the number of sites of the chain a corollary of this conjecture now numerically verified is that pc 1 in the 1 0 limit

secret correlation in repeated games with imperfect monitoring the need for nonstationary strategies the minmax in repeated games with imperfect monitoring can differ from the minmax of those games with perfect monitoring when two or more players are able to gain common information known only to themselves and utilize this information at a later stage gossner and tomala showed that in a class of such games the minmax is given by a weighted average of the payoffs of two main strategies one in which the information is gained and the other in which the information is utilized however all examples analyzed to date require only one main strategy in which information is created and utilized simultaneously we show that two strategies are indeed needed by providing and solving a concrete example of a three player game

critical and off critical conformal analysis of the ising quantum chain in an imaginary field the critical curve with central charge c 22 5 of the ising quantum chain in an imaginary longitudinal field is calculated by finite size extrapolation of the yang lee square root branch point position various power laws are found the field dependence of the off criticality mass scale and the four lowest off criticality scaling functions are calculated the latter turn out to be universal along the critical line and agree very well with the results of the truncated hilbert space method for the c 22 5 continuum theory the author obtains the universal bulk scaling coefficient in qualitative agreement with the thermodynamic bethe ansatz result the scattering phaseshift calculated by luscher s method 1988 reproduces the cardy mussardo minimal solution 1989 for the s matrix if a boundary defect is introduced the only non trivial primary field decouples so that the spectrum consists only of the tower of the unit operator in the antiferromagnetic regime with a non staggered imaginary field the author finds boundary dependent lines where the gap vanishes

the coherent anomaly method and long range one dimensional ising models the authors present the results of the coherent anomaly method when applied to ising models in one dimension with long range interactions this class of systems acts as an interesting and challenging test for the method because the critical exponents as well as the critical temperature values of which are given by the method depend on the rate of fall off of the interactions thus one can see how accurately the method gives results which correctly reflect this dependency the results obtained from this method are compared with results obtained by a variety of other methods

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

some general relations in arbitrary thermostatistics abstract the fundamental thermodynamic relation and the connection between the entropy maximum principle and the energy minimum principle are analyzed in arbitrary thermostatistics in the canonical ensemble it is shown that the relation and connection can occur in very general circumstances furthermore the relation is applied in a nonextensive context and the stability of the tsallis thermostatistics is analyzed

secret correlation in repeated games with imperfect monitoring we characterize the maximum payoff that a team can guarantee against another in a class of repeated games with imperfect monitoring our result relies on the optimal tradeoff for the team between optimization of stage payoffs and generation of signals for future correlation

percolation in networks with long range connections abstract two dimensional lattices of points are connected with long range links whose lengths are distributed according to p r r by changing the decay exponent one can go from d dimensional short range networks to dimensional networks topologically similar to random graphs percolation on these networks is numerically studied for systems of up to 10 7 sites the shortest path fractal and chemical dimensions are determined at the critical threshold as a function of the decay exponent

corner exponents in the two dimensional potts model the critical behavior at a corner in two dimensional ising and three state potts models is studied numerically on the square lattice using transfer operator techniques the local critical exponents for the magnetization and the energy density for various opening angles are deduced from finite size scaling results at the critical point for isotropic or anisotropic couplings the scaling dimensions compare quite well with the values expected from conformal invariance provided the opening angle is replaced by an effective one in anisotropic systems

first order phase transition in potts models with finite range interactions we consider the q state potts model on z d q 3 d 2 with kac ferromagnetic interactions and scaling parameter we prove the existence of a first order phase transition for large but finite potential ranges more precisely we prove that for small enough there is a value of the temperature at which coexist q 1 gibbs states the proof is obtained by a perturbation around mean field using pirogov sinai theory the result is valid in particular for d 2 q 3 in contrast with the case of nearest neighbor interactions for which available results indicate a second order phase transition putting both results together provides an example of a system which undergoes a transition from second to first order phase transition by changing only the finite range of the interaction

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators

determination of the order of phase transitions in potts model by the graph weight approach we examine the order of the phase transition in the potts model by using the graph representation for the partition function which allows treating a non integer number of potts states the order of transition is determined by the analysis of the shape of the graph weight probability distribution the approach is illustrated on special cases of the one dimensional potts model with long range interactions and on its mean field limit