modulated phase of a potts model with competing binary interactions on a cayley tree we study the phase diagram for potts model on a cayley tree with competing nearest neighbor interactions j1 prolonged next nearest neighbor interactions jp and one level next nearest neighbor interactions jo vannimenus proved that the phase diagram of ising model with jo 0 contains a modulated phase as found for similar models on periodic lattices but the multicritical lifshitz point is at zero temperature later mariz et al generalized this result for ising model with jo 0 and recently ganikhodjaev et al proved similar result for the three state potts model with jo 0 we consider potts model with jo 0 and show that for some values of jo the multicritical lifshitz point be at non zero temperature we also prove that as soon as the same level interactionjo is nonzero the paramagnetic phase found at high temperatures for jo 0 disappears while ising model does not obtain such property to perform this study an iterative scheme similar to that appearing in real space renormalization group frameworks is established it recovers as particular case previous work by ganikhodjaev et al for jo 0 at vanishing temperature the phase diagram is fully determined for all values and signs of j1 jp and jo at finite temperatures several interesting features are exhibited for typical values of jo j1

the asymmetric clock model on a cayley tree the asymmetric clock model is studied on a cayley tree and commensurate and incommensurate phases are found the transition lines are obtained from stability conditions and characteristic points in the phase diagram are analysed by numerical iteration a critical endpoint is found for the case of three states per site and a lifshitz point for the case of four states per site

on the integrability of 2 1 dimensional quasilinear systems a 2 1 dimensional quasilinear system is said to be integrable if it can be decoupled in infinitely many ways into a pair of compatible n component one dimensional systems in riemann invariants exact solutions described by these reductions known as nonlinear interactions of planar simple waves can be viewed as natural dispersionless analogues of n gap solutions it is demonstrated that the requirement of the existence of sufficiently many n component reductions provides the effective classification criterion as an example of this approach we classify integrable 2 1 dimensional systems of conservation laws possessing a convex quadratic entropy

n soliton solutions to the dkp equation and weyl group actions we study soliton solutions to the dkp equation which is defined by the hirota bilinear form where 0 1 the functions n are given by the pfaffians of a certain skew symmetric matrix we identify a one soliton solution as an element of the weyl group of d type and discuss a general structure of the interaction patterns among the solitons soliton solutions are characterized by a 4n 4n skew symmetric constant matrix which we call the b matrix we then find that one can have m soliton solutions with m being any number from n to 2n 1 for some of the 4n 4n b matrices having only 2n nonzero entries in the upper triangular part the number of solitons obtained from those b matrices was previously expected to be just n

phase diagrams of competing quadruple and binary interactions on cayley tree like lattice triangular chandelier abstract we study the phase diagrams for the ising model on a cayley tree like lattice called triangular chandelier with competing nearest neighbour interactions j 1 prolonged next nearest neighbour interactions j p and one level next nearest neighbour quadruple interactions j l 1 the phase diagrams display the multicritical points the lifshitz points that are at nonzero temperature and many modulated phases to perform this study an iterative scheme similar to that appearing in real space renormalization group frameworks is established it recovers as particular case previous work of vannimenus extension result given by ganikhodjaev and uguz for k 3 at vanishing temperature the phase diagram is fully determined for all values and signs of j 1 j p and j l 1 at finite temperatures several interesting features are exhibited for typical values of j l 1 j 1 and j p j 1

phase diagram of the ising model on a cayley tree in the presence of competing interactions and magnetic field we study the phase diagram for the ising model on a cayley tree with competing nearest neighbor interactionsj1 and next nearest neighbor interactionsj2 andj3 in the presence of an external magnetic field to perform this study an iterative scheme similar to that appearing in real space renormalization group frameworks is established it recovers as particular cases previous works by vannimenus and by inawashiroet al at vanishing temperature the phase diagram is fully determined for all values and signs ofj2 j1 andj3 j2 in particular we verify that values ofj3 j2 high enough favor the paramagnetic phase at finite temperatures several interesting features evolution of reentrances separation of the modulated region into two disconnected pieces etc are exhibited for typical values ofj2 j1 andj3 j2

on gibbs measures of models with competing ternary and binary interactions and corresponding von neumann algebras in the present paper the ising model with competing binary j and binary j1 interactions with spin values 1 on a cayley tree of order 2 is considered the structure of gibbs measures for the model is studied we completely describe the set of all periodic gibbs easures for the model with respect to any normal subgroup of finite index of a group representation of the cayley tree types of von neumann algebras generated by gns representation associated with diagonal states corresponding to the translation invariant gibbs measures are determined it is proved that the factors associated with minimal and maximal gibbs states are isomorphic and if they are of type iii then the factor associated with the unordered phase of the model can be considered as a subfactors of these factors respectively some concrete examples of factors are given too

exact solution of an ising model with competing interactions on a cayley tree the exact solution of an ising model with competing restricted interactions on the cayley tree and in the absence of an external field is presented a critical curve is defined where it is possible to get phase transitions above it and a single gibbs state is obtained elsewhere

on various solutions of the coupled kp equation the coupled kp ckp equation possesses n soliton solutions with many more degrees of freedom than the solitons for the usual kp equation have in comparison ckp solutions can therefore be expected to model far more complex interactions than their kp counterparts in this paper we present some typical solutions for the ckp system and for some of its reductions a complex coupled kdv equation and a coupled boussinesq equation and we analyse their interaction and asymptotic properties

technical note analysis of a preference order traveling salesman problem application is made to the preference order dynamic programming solution procedure proposed by kao for a stochastic traveling salesman problem although the procedure is flawed from the myopic interpretation of the monotonicity condition it may be used as a convenient heuristic tool for solving stochastic problems

on contour arguments for the three state potts model with competing interactions on a semi infinite cayley tree we consider the potts model with competing two step interactions and spin values 1 2 3 on a semi infinite cayley tree of order 2 we describe ground states and verify the peierls condition for the model using a contour argument we show the existence of three different gibbs measures associated with translation invariant ground states

phase diagrams of ising models on husimi trees i pure multisite interaction systems lattice spin systems with multisite interactions have rich and interesting phase diagrams we present some results for such systems involving ising spins 1 using a generalization of the bethe lattice approximation first we show that our approach yields good approximations for the phase diagrams of some recently studied multisite interaction systems second a multisite interaction system with competing interactions is investigated and a strong connection with results from the theory of dynamical systems is made we exhibit a full bifurcation diagram chaos period 3 windows etc for the magnetization of the base site of this system

competing binary and k tuple interactions on a cayley tree of arbitrary order abstract we study the phase diagram for the ising model on a cayley tree of arbitrary order k with competing nearest neighbor interactions j 1 prolonged next nearest neighbor interactions j p and one level k tuple neighbor interaction j o the phase diagram is studied for several ranges of the competing parameters it shows the appearance of several features and modulated phases arising from the frustration effects introduced by the one level k tuple neighbor interaction j o the variation of the wavevector with temperature in the modulate phase is studied in detail it shows narrow commensurate steps between incommensurate regions finally the lyapunov exponent associated with the trajectory of the system is investigated

simple ising models still thrive a review of some recent progress abstract a selection of recent work by various authors concerning spin 1 2 ising modls with pair couplings is reviewed topics addressed include the universality of corrections to scaling and nonlinear scaling fields in planar ising models aspects of many particle correlation functions the testing and verification of scaling hypotheses for local magnetizations in the presence of walls and boundaries including the singular nature of the critical region scaling functions and the decay of the influence of a far wall a soluble model of a surface roughening transition nonuniversal critical effects of one dimensional perturbations in planar ising models the effects of spatially anisotropic further neighbor interactions in particular annni models in d 2 dimensions and soluble mock annni models in 2 and 3 dimensions

quantum painleve calogero correspondence for painleve vi this paper is a continuation of our previous paper where the painleve calogero correspondence has been extended to auxiliary linear problems associated with painleve equations we have proved for the first five equations from the painleve list that one of the linear problems can be recast in the form of the non stationary schrodinger equation whose hamiltonian is a natural quantization of the classical calogero like hamiltonian for the corresponding painleve equation in the present paper we establish the quantum painleve calogero correspondence for the most general case the painleve vi equation we also show how the desired special gauge and the needed choice of variables can be derived starting from the corresponding schlesinger system with rational spectral parameter

statistical mechanics of z m models on cayley trees abstract the problem of small field phase transitions for z m models on cayley trees is solved in detail phase diagrams for zero field are obtained for m 2 3 4 5 and 6 as special cases potts models are also considered and all phases not only those in zero field are identified the m limit the planar rotator model is also solved completely for the zero field case the relevance of the results especially of the phase diagrams for the problems associated with z m models on real lattices is discussed

strange attractor in the ising model with competing interactions on the cayley tree on formule le modele d ising avec interactions de competition sur un arbre de cayley comme une application non lineaire a 2 dimensions

toda lattice hierarchy and conservation laws time evolutions of the toda lattice hierarchies of ueno and takasaki are induced by hamiltonians which are conservation laws for the original one and two dimensional toda lattice obtained by olive and turok moreover these hamiltonians for two dimensional toda lattice hierarchy are also conserved quantities of the two component kp hierarchy in which that system is embedded the one dimensional toda lattice hierarchy is characterized by the bilinear relations and a new version of the one dimensional toda lattice hierarchy is constructed generalized toda lattice hierarchies associated to all affine lie algebras are presented

algebro geometric approach in the theory of integrable hydrodynamic type systems the algebro geometric approach for integrability of semi hamiltonian hydrodynamic type systems is presented the class of symmetric hydrodynamic type systems is defined and the calculation of the associated riemann surfaces is greatly simplified for this class many interesting and physically motivated examples are investigated

ising model with competing interactions on a cayley tree an iterative scheme is developed for a renormalized effective nearest neighbor couplingk r and effective field per sitek r for spins in therth shell of a cayley tree with nearest neighborj and next nearest neighborj interactions between ising spins on the lattice in addition to the expected paramagnetic ferromagnetic and antiferromagnetic phases we find an intermediate range ofj j 0 values wherex r and kr iterate to a continuous or quasicontinuous attractor in thex k plane in this range the local magnetization is mainly chaotic with oscillatory glasslike behavior embedded in the chaos however are regions of periodic and commensurate phases

integrable structure of the dirichlet boundary problem in multiply connected domains we study the integrable structure of the dirichlet boundary problem in two dimensions and extend the approach to the case of planar multiply connected domains the solution to the dirichlet boundary problem in the multiply connected case is given through a quasiclassical tau function which generalizes the tau function of the dispersionless toda hierarchy it is shown to obey an infinite hierarchy of hirota like equations which directly follow from properties of the dirichlet green function and from the fay identities the relation to multi support solutions of matrix models is briefly discussed