Related papers: Potts Glass on Random Graphs
We consider the Potts model on a two-dimensional periodic rectangular lattice with general coupling constants $J_{ij}>0$, where $i,j\in\{1,2,3\}$ are the possible spin values (or colors). The resulting energy landscape is thus significantly…
An asymmetric generalization of the zero-temperature q-state Potts model on a one dimensional lattice, with and without boundaries, has been studied. The dynamics of the particle number, and specially the large time behavior of the system…
The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some degrees of freedom remain disordered.…
Phase transitions in spin glass type systems and, more recently, in related computational problems have gained broad interest in disparate arenas. In the current work, we focus on the "community detection" problem when cast in terms of a…
We study the antiferromagnetic $q$-state Potts model on the square lattice for $q=3$ and $q=4$, using the Wang-Swendsen-Koteck\'y Monte Carlo algorithm and a new finite-size-scaling extrapolation method. For $q=3$ we obtain good control up…
We investigate the properties of the glass phase of a recently introduced spin glass model of soft spins subjected to an anharmonic quartic local potential, which serves as a model of low temperature molecular or soft glasses. We solve the…
The low-temperature instability of one-step replica symmetry breaking (1RSB) phase in 3-state Potts spin glass is obtained explicitly. The temperature of the instability is higher than the temperature where the 1RSB entropy becomes…
We investigate the p-state mean-field model of the Potts glass ($2\le p \le 4$) below the continuous phase transition to a glassy phase. We find that apart from a solution with a first hierarchical level of replica-symmetry breaking (1RSB),…
In this survey, we give a friendly introduction from a graph theory perspective to the q-state Potts model, an important statistical mechanics tool for analyzing complex systems in which nearest neighbor interactions determine the aggregate…
We present exact results on the partition function of the $q$-state Potts model on various families of graphs $G$ in a generalized external magnetic field that favors or disfavors spin values in a subset $I_s = \{1,...,s\}$ of the total set…
We investigate the quenching process in lattice systems with short range interaction and several crystalline states as ground states. We consider in particular the following systems on square lattice: - hard particle (exclusion) model; - q…
The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics the same way the random energy model clarifies spin glass behavior would…
We propose a new analytic approach to study the phase diagram of random heteropolymers, based on the cavity method. For copolymers we analyze the nature and phenomenology of the glass transition as a function of sequence correlations.…
We construct the exact partition function of the Potts model on a complete graph subject to external fields with linear and nematic type couplings. The partition function is obtained as a solution to a linear diffusion equation and the free…
We consider a Lattice Gas model in which the sites interact via infinite-ranged random couplings independently distributed with a Gaussian probability density. This is the Lattice Gas analogue of the well known Sherrington-Kirkpatrick Ising…
Distinctive orderings and phase diagram structures are found, from renormalization-group theory, for odd q-state clock spin-glass models in d=3 dimensions. These models exhibit asymmetric phase diagrams, as is also the case for quantum…
Finite-size effects in the mean-field Ising spin glass and the mean-field three-state Potts glass are investigated by Monte Carlo simulations. In the thermodynamic limit, each model is known to exhibit a continuous phase transition into the…
The Kondo lattice model has been analyzed in the presence of a random inter-site interaction among localized spins with non zero mean Jo and standard deviation J. Following the same framework previously introduced by us, the problem is…
We introduce a new disordered system, the Super-Potts model, which is a more frustrated version of the Potts glass. Its elementary degrees of freedom are variables that can take M values and are coupled via pair-wise interactions. Its exact…
We study the L\'evy spin-glass model with the replica and the cavity method. In this model each spin interacts through a finite number of strong bonds and an infinite number of weak bonds. This hybrid behaviour of L\'evy spin glasses…