the droplet in the tube a case of phase transition in the canonical ensemble we consider the 2 dimensional ising model with ferromagnetic nearest neighbour interaction at inverse temperature lets n t be the total magnetization inside ann n square box per be the gibbs state in with periodic b c andm be the spontaneous magnetization we show the existence of the limit psi varrho mathop lim limits n to infty left frac 1 beta n right ln mu lambda per s n n varrho for m provided is large enough it turns out that the quantity is closely related to the wulf construction and the dependence of the function on is singular

well structured transition systems everywhere well structured transition systems wstss are a general class of infinite state systems for which decidability results rely on the existence of a well quasi ordering between states that is compatible with the transitions in this article we provide an extensive treatment of the wsts idea and show several new results our improved definitions allow many examples of classical systems to be seen as instances of wstss

large deviations for the 2d ising model a lower bound without cluster expansions we show that a lower large deviation bound for the block spin magnetization in the 2d ising model can be pushed all the way forward toward its correct wulff value for all c

large deviations and continuum limit in the 2d ising model we study the 2d ising model in a rectangular box l of linear size o l we determine the exact asymptotic behaviour of the large deviations of the magnetization p t2 l ae t when l 1 for values of the parameters of the model corresponding to the phase coexistence region where the order parameter m is strictly positive we study in particular boundary eects due to an arbitrary real valued boundary magnetic field using the self duality of the model a large part of the analysis consists in deriving properties of the covariance function hae 0 ae t i as t 1 at dual values of the parameters of the model to do this analysis we establish new results about the high temperature representation of the model these results are valid for dimensions d 2 and up to the critical temperature they give a complete non perturbative exposition of the high temperature representation we then study the gibbs measure conditioned by p t2 l ae t im l l l ic with 0 c 1 4 and im m m we construct the continuum limit of the model and describe the limit by the solutions of a variational problem of isoperi metric type

equilibrium shapes of crystals attached to walls we discuss equilibrium shapes of crystals attached to walls optimal shapes for different configurations of walls are found and the minimality of the overall surface tension is proven with the help of a simple geometrical argument based on the isoperimetric inequality and monotonicity stability results in the form of bonnesen inequalities are obtained in the two dimensional case

constrained variational problem with applications to the ising model we continue our study of the behavior of the two dimensional nearest neighbor ferromagnetic ising model under an external magnetic fieldh initiated in our earlier work we strengthen further a result previously proven by martirosyan at low enough temperature which roughly states that for finite systems with boundary conditions under a positive external field the boundary effect dominates in the system if the linear size of the system is of orderb h withb small enough while ifb is large enough then the external field dominates in the system in our earlier work this result was extended to every subcritical value of the temperature here for every subcritical value of the temperature we show the existence of a critical valueb0 t which separates the two regimes specified above we also find the asymptotic shape of the region occupied by the phase in the second regime which turns out to be a squeezed wulff shape the main step in our study is the solution of the variational problem of finding the curve minimizing the wulff functional which curve is constrained to the unit square other tools used are the results and techniques developed to study large deviations for the block magnetization in the absence of the magnetic field extended to all temperatures below the critical one

on the expressive power of movement and restriction in pure mobile ambients pure mobile ambients is a process calculus suitable to focus on issues related to mobility abstracting away from aspects concerning process communication however it incorporates name restriction i e the vn binder and ambient movement i e the in and out capabilities that can be seen as characteristics adapted or directly borrowed from the tradition of communication based process calculi for this reason we retain that it is worth to investigate whether or not these features can be removed from pure mobile ambients without losing expressive power to this aim we consider two variants of pure mobile ambients which differ in the way infinite processes can be defined the former exploits process replication while the latter is more general and permits recursive process definition we analyse whether or not the elimination of ambient movement and or name restriction reduces the expressive power of these two calculi using the decidability of process termination as a yardstick we prove that name restriction can be removed from both calculi without reducing the expressive power on the other hand the elimination of both ambient movement and name restriction strictly reduces the expressive power of both calculi as far as the elimination of only ambient movement is concerned we prove an interesting discrimination result process termination is undecidable under recursive process definition while it turns out to be decidable under process replication

approximation of subadditive functions and convergence rates in limiting shape results for a nonnegative subadditive function h on mathbb z d with limiting approximation g x lim n h nx n it is of interest to obtain bounds on the discrepancy between g x and h x typically of order x nu with nu 1 for certain subadditive h x particularly those which are expectations associated with optimal random paths from 0 to x in a somewhat standardized way a more natural and seemingly weaker property can be established every x is in a bounded multiple of the convex hull of the set of sites satisfying a similar bound we show that this convex hull property implies the desired bound for all x applications include rates of convergence in limiting shape results for first passage percolation standard and oriented and longest common subsequences and bounds on the error in the exponential decay approximation to the off axis connectivity function for subcritical bernoulli bond percolation on the integer lattice

power law corrections to exponential decay of connectivities and correlations in lattice models consider a translation invariant bond percolation model on the integer lattice which has exponential decay of connectivities that is the probability of a connection 0 x by a path of open bonds decreases like exp m x for some positive constant m which may depend on the direction x x in two and three dimensions it is shown that if the model has an appropriate mixing property and satisfies a special case of the fkg property then there is at most a power law correction to the exponential decay there exist a and c such that exp m x p 0 x a x c exp m x for all nonzero x in four or more dimensions a similar bound holds with x c replaced by exp c log x 2 in particular the power law lower bound holds for the fortuin kasteleyn random cluster model in two dimensions whenever the connectivity decays exponentially since the mixing property is known to hold in that case consequently a similar bound holds for correlations in the potts model at supercritical temperatures

on weak mixing in lattice models for lattice models on d weak mixing is the property that the influence of the boundary condition on a finite decays exponentially with distance from that region for a wide class of models on 2 including all finite range models we show that weak mixing is a consequence of gibbs uniqueness exponential decay of an appropriate form of connectivity and a natural coupling property in particular on 2 the fortuin kasteleyn random cluster model is weak mixing whenever uniqueness holds and the connectivity decays exponentially and the q state potts model above the critical temperature is weak mixing whenever correlations decay exponentially a hypothesis satisfied if q is sufficiently large ratio weak mixing is the property that uniformly over events a and b occurring on subsets and respectively of the lattice p a b p a p b 1 decreases exponentially in the distance between and we show that under mild hypotheses for example finite range weak mixing implies ratio weak mixing

existence of gauge field in any partially integrable systems for any integrable and more generally any partially integrable model the existence is shown of a yang mills gauge field with zero curvature whose gauge group consists of all general coordinate transformations it has been suggested that this fact may have some connection with existence of an affine connection in the space with zero riemann curvature tensor a brst like quadratically nilpotent operator is also constructed for any theory with poisson bracket structure whenever such a connection with zero riemann curvature exists

stability of the wulff minimum and fluctuations in shape for large finite clusters in two dimensional percolation for two dimensional bernoulli percolation at densityp above the critical point there exists a natural normg determined by the rate of decay of the connectivity function in every direction ifw is the region of unit area with boundary of minimum possibleg length then it is known 4 that asn with probability approaching 1 conditionally onn c 0 0 if is a curve enclosing a region of unit area such that the hausdorff distanced h v dw for every translate v then theg lengthg g w k 2 at least for small

ornstein zernike theory for the bernoulli bond percolation on mathbb z d we derive a precise ornstein zernike asymptotic formula for the decay of the two point function p p 0 x of the bernoulli bond percolation on the integer lattice z d in any dimension d 2 in any direction x and for any subcritical value of p p c d

surface order large deviations for high density percolation we derive surface order large deviation estimates for the volume of the largest cluster and for the volume of the largest region surrounded by a cluster of a bernoulli percolation process restricted to a big finite box with sufficiently large parameter we also establish a useful version of the isoperimetric inequality which is the main tool of our proofs

dobrushin kotecký shlosman theorem up to the critical temperature we develop a non perturbative version of the dobrushin koteck shlosman theory of phase separation in the canonical 2d ising ensemble the results are valid for all temperatures below critical

second order large deviation estimates for ferromagnetic systems in the phase coexistence region we consider thed dimensional ising model with ferromagnetic nearest neighbor interaction at inverse temperature let m lambda lambda 1 sum limits i in lambda sigma i be the magnetization inside ad dimensional hyper cube be the gibbs state andm be the spontaneous magnetization for such thatm 0 we find a sufficient condition easily verified to hold for large for m a b to decay exponentially with d 1 d when m b m 1 a b ford 2 this sufficient condition is the exponential decay of a connectivity function we also prove a partial converse to this result obtain a sharper result for the magnetization ond 1 dimensional cross sections of the model and prove a similar result ford 2 m a b m and large when free boundary conditions are chosen outside

theory of interaction abstract theory of interaction aims to provide a foundational framework for computation and interaction it proposes four fundamental principles that characterize the common features of all models of computation and interaction these principles suffice to support a model independent treatment of the two most important relationships in computer science the equality between processes and the relative expressiveness between models based on the two relationships the theory of equality the theory of expressiveness and the theory of completeness are developed

nijenhuis bianchi identity and brst like operators let m be a differentiable manifold with a 1 1 tensor field s x a notion of distorted torsion tensor is introduced that reduces to the ordinary torsion tensor when s it is then shown that the distorted torsion tensor satisfies a generalization of the first bianchi identity the new identity involves the nijenhuis tensor in contrast to the standard bianchi identity using this generalized formula brst like operators are constructed that satisfy a lie super algebra when both nijenhuis and riemann tensors vanish identically

symmetric electoral systems for ambient calculi this paper compares the expressiveness of different fragments of ambient calculi via leader election problems we consider mobile ambients ma safe ambients sa and the push and pull ambient calculus pac cardelli and gordon encoded the asynchronous p calculus into ma zimmer has shown that the synchronous p calculus without choice can be encoded in pure no communication sa we show that pure ma without restriction has symmetric electoral systems that is it is possible to solve the problem of electing a leader in a symmetric network by the work of palamidessi this implies that this fragment of ma is not encodable under certain conditions in the p calculus with separate choice moreover we use the same technique to show that fragments of sa and pac are not encodable under certain conditions in the p calculus with separate choice we also show that particular fragments of ambient calculi do not admit a solution to leader election problems in the same way as the p calculus with separate choice this yields a fine grained hierarchy within ambient calculi

complete analyticity for 2d ising completed we study the behavior of the two dimensional nearest neighbor ferromagnetic ising model under an external magnetic fieldh we extend to every subcritical value of the temperature a result previously proven by martirosyan at low enough temperature and which roughly states that for finite systems with boundary conditions under a positive external field the boundary effect dominates in the bulk if the linear size of the system is of orderb h withb small enough while ifb is large enough then the external field dominates in the bulk as a consequence we are able to complete the proof that complete analyticity for nice sets holds for every value of the temperature and external field in the interior of the uniqueness region in the phase diagram of the model the main tools used are the results and techniques developed to study large deviations for the block magnetization in the absence of the magnetic field and recently extended to all temperatures below the critical one by ioffe

surface order large deviations for ising potts and percolation models we derive uniform surface order large deviation estimates for the block magnetization in finite volume ising or potts models with plus or free or a combination of both boundary conditions in the phase coexistence regime ford 3 the results are valid up to a limit of slab thresholds conjectured to agree with the critical temperature our arguments are based on the renormalization of the random cluster model withq 1 andd 3 and on corresponding large deviation estimates for the occurrence in a box of a largest cluster with density close to the percolation probability the results are new even for the case of independent percolation q 1 as a byproduct of our methods we obtain further results in the fk model concerning semicontinuity inp andq of the percolation probability the second largest cluster in a box and the tail of the finite cluster size distribution

integrable dynamical systems with hierarchy i formulation it is shown that any model with the zero generalized nijenhuis tensor under some additional assumptions will automatically satisfy the hierarchy equation with an infinite number of conserved quantities in involution especially if there is a dual symplectic structure with zero nijenhuis tensor then there exist infinite numbers of poisson brackets and of lagrangians giving the same equation of motion toda lattice is one such example

gaussian fluctuations of connectivities in the subcritical regime of percolation we consider thed dimensional bernoulli bond percolation model and prove the following results for allp pc the finite volume conditional measures defined by requiring the existence of a dual path between opposing faces of the boundary converge in the infinite volume limit to the standard bernoulli measure

decoding choice encodings we study two encodings of the asynchronous calculus with input guarded choice into its choice free fragment one encoding is divergence free but refines the atomic commitment of choice into gradual commitment the other preserves atomicity but introduces divergence the divergent encoding is fully abstract with respect to weak bisimulation but the more natural divergence free encoding is not instead we show that it is fully abstract with respect to coupled simulation a slightly coarser but still coinductively defined equivalence that does not enforce bisimilarity of internal branching decisions the correctness proofs for the two choice encodings introduce a novel proof tech nique exploiting the properties of explicit decodings from translations to source terms

on the expressiveness of interaction subbisimilarity is proposed as a general tool to classify the relative expressive power of process calculi the expressiveness of several variants of ccs is compared in terms of the subbisimilarity relationship similar investigation is also carried out for the variants of the pi calculus the relative expressiveness of the different forms of the choice operation and the different ways of introducing infinite behaviors are systematically studied in both the frameworks of ccs and pi some issues concerning the expressiveness of both ccs and pi are clarified several open problems are solved along the way the subbisimilarity approach and the relative expressiveness results are applied to show the independence of the operators of the pi calculus the definition of the subbisimilarity relationship can be further strengthened with computational requirement leading to a uniform treatment of computation and interaction

on the two dimensional stochastic ising model in the phase coexistence region near the critical point we consider the two dimensional stochastic ising model in finite square with free boundary conditions at inverse temperature 0 and zero external field using duality and recent results of ioffe on the wulff construction close to the critical temperature we extend some of the results obtained by martinelli in the low temperature regime to any temperature below the critical one in particular we show that the gap in the spectrum of the generator of the dynamics goes to zero in the thermodynamic limit as an exponential of the side length of with a rate constant determined by the surface tension along one of the coordinate axes we also extend to the same range of temperatures the result due to shlosman on the equilibrium large deviations of the magnetization with free boundary conditions

the wulff construction and asymptotics of the finite cluster distribution for two dimensional bernoulli percolation we consider two dimensional bernoulli percolation at densityp p c and establish the following results