Related papers: Interface mapping in two-dimensional random lattic…

We describe a simple nearest-neighbor Ising model that is capable of supporting a gas, liquid, crystal, in characteristic relationship to each other. As the parameters of the model are varied one obtains characteristic patterns of phase…

In a recent paper [Phys. Rev. Lett. 129, 120601] we have shown that the dynamics of interfaces, in the symmetry-broken phase of the two-dimensional ferromagnetic quantum Ising model, displays a robust form of ergodicity breaking. In this…

The sensitivity of the random field Ising model to small random perturbations of the quenched disorder is studied via exact ground states obtained with a maximum-flow algorithm. In one and two space dimensions we find a mild form of chaos,…

We study the dynamics of the travelling interface arising from a bistable piece-wise linear one-way coupled map lattice. We show how the dynamics of the interfacial sites, separating the two superstable phases of the local map, is finite…

A recently introduced model describing the folding of the triangular lattice is generalized allowing for defects in the lattice and written as an Ising model with nearest-neighbor and plaquette interactions on the honeycomb lattice. Its…

We study the equilibrium properties of an Ising model on a disordered random network where the disorder can be quenched or annealed. The network consists of four-fold coordinated sites connected via variable length one-dimensional chains.…

For the generalized Ising models with all possible interactions within a face of the square lattice the formulas for finding partition function and free energy per lattice site in the thermodynamic limit were derived on a certain, in the…

I show that the cluster variation method, long used as a powerful hierarchy of approximations for discrete (Ising-like) two-dimensional lattice models, yields exact results on the disorder varieties which appear when competitive…

We present a numerical study of the dynamics of a non-ideal fluid subject to a density-dependent pseudo-potential characterized by a hierarchy of nested attractive and repulsive interactions. It is shown that above a critical threshold of…

We report on single-cluster Monte Carlo simulations of the Ising, 4-state Potts and 10-state Potts models on quenched ensembles of planar, tri-valent random graphs. We confirm that the first-order phase transition of the 10-state Potts…

A relation between O(n) lattice spin models and Ising models defined on the same lattice was recently put forward [L. Casetti, C. Nardini, and R. Nerattini, Phys. Rev. Lett. 106, 057208 (2011)]. Such a relation, inspired by an energy…

We review some of the recent results on two-interacting particles (TIP) in low-dimensional disordered quantum models. Special attention is given to the mapping of the problem onto random band matrices. In particular, we construct two…

We compute properties of the interface of the 3-dimensional Ising model for a wide range of temperatures, covering the whole region from the low temperature domain through the roughening transition to the bulk critical point. The interface…

The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While…

We introduce lattice models with explicit N=2 supersymmetry. In these interacting models, the supersymmetry generators Q^+ and Q^- yield the Hamiltonian H={Q^+,Q^-} on any graph. The degrees of freedom can be described as either fermions…

We present a numerical determination of the order-disorder interface tension, \sod, for the two-dimensional seven-state Potts model. We find $\sod=0.0114\pm0.0012$, in good agreement with expectations based on the conjecture of perfect…

An introduction to the application of combinatorial optimization methods to ground state calculations of frustrated, disordered systems is given. We discuss the interface problem in the random bond Ising ferromagnet, the random field Ising…

We analyse features of the patterns formed from a simple model for a martensitic phase transition. This is a fragmentation model that can be encoded by a general branching random walk. An important quantity is the distribution of the…

We study the phenomenon of intermittency in inhomogeneous lattices of coupled map where inhomogeneity appears in the form of different values of map parameters at adjacent sites.The system exhibits spatiotemporal intermittency in various…

We note that it is possible to construct a bond vertex model that displays q-state Potts criticality on an ensemble of phi3 random graphs of arbitrary topology, which we denote as ``thin'' random graphs in contrast to the fat graphs of the…