We present here new evidence that after a quench the planar Potts model on the square lattice relaxes towards a glassy state if the number of states q is larger than four. By extrapolating the finite size data we compute the average energy of these states for the infinite system with periodic boundary conditions, and find that it is comparable with that previously found using fixed boundary con...

Nucleation theory [l-4] deals with that general class of phenomena which can be mapped onto the familiar condensation of a supercooled vapor and, in its present form, it heavily rests’upon the concept of clusters (droplets, grains, etc.). Although a set of basic ideas is now rather well-established, the theory still uses many phenomenological ideas and approximations so that, in order to minimi...

A new approach to derivation of various effective-field approximations for lattice spin models in a unique way is presented. It is shown that it can give a number of methods, including the DMRG method, that can be used to find generally inhomogeneous solutions of 2D classical lattice problems. A method, closely related to the DMRG method but without necessity to perform spin renormal-ization, i...

The security of lattice-based cryptosystems such as NTRU, GGH and Ajtai-Dwork essentially relies upon the intractability of computing a shortest non-zero lattice vector and a closest lattice vector to a given target vector in high dimensions. The best algorithms for these tasks are due to Kannan, and, though remarkably simple, their complexity estimates have not been improved since more than tw...

Selecting parameters in lattice-based cryptography is a challenging task, which is essentially accomplished using one of two approaches. The first (very common) approach is to derive parameters assuming that the desired security level is equivalent to the bit hardness of the underlying lattice problem, ignoring the gap implied by available security reductions. The second (barely used) approach ...

We present a numerical method, based on exact series expansions, that distinguishes between lattice-based models both in combinatorics and statistical mechanics that are likely to be solvable in terms of simple functions of mathematical physics, and those that possess a natural boundary in a suitably de ned complex plane. This latter class cannot therefore be algebraic, nor di erentiably nite n...

We show that the one-dimensional lattice model proposed by Lipatov to describe the high energy scattering of hadrons in multicolor QCD is completely integrable. We identify this model as the XXX Heisenberg chain of noncompact spin s = 0 and find the conservation laws of the model. A generalized Bethe ansatz is developed for the diagonalization of the hamiltonian and for the calculation of hadro...

the present study has been conducted on shemiranat county landscape, using lattice hexagon approach, for the first time, in order to achieve homogeneous units in degradation model. to this aim, with respect to the extent of the studied area, a lattice hexagon composed of 36 units (cells) was created and each grid cell was considered as a sub landscape. next, ecological vulnerability, degradatio...