Related papers: Non-robust phase transitions in the generalized cl…
We study several statistical mechanical models on a general tree. Particular attention is devoted to the classical Heisenberg models, where the state space is the d-dimensional unit sphere and the interactions are proportional to the…
We point out that the high-q Potts model on a regular lattice at its transition temperature provides an example of a non-robust - in the sense recently proposed by Pemantle and Steif- phase transition.
We prove an inequality on decision trees on monotonic measures which generalizes the OSSS inequality on product spaces. As an application, we use this inequality to prove a number of new results on lattice spin models and their…
We present a numerical study of the self-affine profiles obtained from configurations of the q-state Potts (with q=2,3 and 7) and p=10 clock models as well as from the occupation states for site-percolation on the square lattice. The first…
The influence of uncorrelated, quenched disorder on the phase transition of two dimensional Potts models will be reviewed. After an introduction where the conditions of relevance of quenched randomness on phase transitions are exemplified…
The random quantum $q$-state clock and Potts models are studied in 2 and 3 dimensions. The existence of Griffiths phases is tested in the 2D case with $q=6$ by sampling the integrated probability distribution of local susceptibilities of…
We study zero temperature phase transitions in two classes of random quantum systems -the $q$-state quantum Potts and clock models. For models with purely ferromagnetic interactions in one dimension, we show that for strong randomness there…
The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described…
We formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical…
Phase transition in the two-dimensional $q$-state Potts model with random ferromagnetic couplings in the large-q limit is conjectured to be described by the isotropic version of the infinite randomness fixed point of the random…
In the present paper we shall consider countable state $p$-adic Potts model on $Z_+$. A main aim is to establish the existence of the phase transition for the model. In our study, we essentially use one dimensionality of the model. To show…
The Potts model with invisible states was introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where $Z_q$ symmetry is spontaneously broken. It differs from…
In the present paper we study a phase transition problem for the Potts model with three competing interactions, the nearest neighbors, the second neighbors and triples of neighbors and non-zero external field on Cayley tree of order two. We…
The Potts model describes interacting spins with $Q$ different components, which is a direct generalization of the Ising model ($Q=2$). Compared to the existing exact solutions in 2D, the phase transitions and critical phenomena in the 3D…
We analyze the ways in which the random first order phase transition (RFOT) of the glass transition differs from the well-studied regular first order and second order (or continuous) phase transitions. Just as is the case in the latter two…
The nature of phase transitions involving the questions why and how phase transitions take place has not been sufficiently touched in the literature. In contrast, the current attention to certain extent still focus on the description of…
A fundamental dichotomous classification for all physical systems is according to whether they are spinless or spinful. This is especially crucial for the study of symmetry-protected topological phases, as the two classes have distinct…
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…
We study the two-dimensional Potts model on the square lattice in the presence of quenched random-bond impurities. For q>4 the first-order transitions of the pure model are softened due to the impurities, and we determine the resulting…
Mixed order phase transitions (MOT), which display discontinuous order parameter and diverging correlation length, appear in several seemingly unrelated settings ranging from equilibrium models with long-range interactions to models far…