Related papers: A classification of four-state spin edge Potts mod…
Topological spin liquids are robust quantum states of matter with long-range entanglement and possess many exotic properties such as the fractional statistics of the elementary excitations. Yet these states, short of local parameters like…
This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper…
We generalize the classical one dimensional Potts model to the case where the symmetry group is a non-Abelian finite group. It turns out that this new model has a quantum nature in that its spectrum of energy eigenstates consists of…
The analysis of correlation function data obtained by Monte Carlo simulations of the two-dimensional 4-state Potts model, XY model, and self-dual disordered Ising model at criticality are presented. We study the logarithmic corrections to…
We set out to explore the possibility of investigating the critical behavior of systems with first-order phase transition using deep machine learning. We propose a machine learning protocol with ternary classification of instantaneous spin…
The three-state Potts model is numerically investigated on three-dimensional simple cubic lattices of up to \(128^3\) volume, concentrating on the neighborhood of the first-order phase transition separating the ordered and disordered…
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…
In this paper, we consider the parameterization of the spectra of the three-state critical Potts quantum chain with integrable twisted boundary conditions in terms of Bethe ansatz type equations. The Bethe equations are found by…
Dynamic processes of interacting units on a network are out of equilibrium in general. In the case of a directed tree, the dynamic cavity method provides an efficient tool that characterises the dynamic trajectory of the process for the…
The two-dimensional $Q$-state Potts model with real couplings has a first-order transition for $Q>4$. We study a loop-model realization in which $Q$ is a continuous parameter. This model allows for the collision of a critical and a…
We consider q-state Potts models coupled by their energy operators. Restricting our study to self-dual couplings, numerical simulations demonstrate the existence of non-trivial fixed points for 2 <= q <= 4. These fixed points were first…
Ising's solution of a classical spin model famously demonstrated the absence of a positive-temperature phase transition in one-dimensional equilibrium systems with short-range interactions. No-go arguments established that the energy cost…
We present a methodology that extends invariant manifold theory to a class of autonomous piecewise linear systems with nonsmoothness at the equilibrium, providing a framework for model order reduction in mechanical structures with compliant…
Exploiting the azimuthal angle dependence of the density matrices we construct observables that directly measure the spin of a heavy unstable particle. A novelty of the approach is that the analysis of the azimuthal angle dependence in a…
We studied the long-term nonequilibrium dynamics of $q$-state Potts models with $q=4$, $5$, $6$, and $8$ using Monte Carlo simulations on a two-dimensional square lattice. When the contact energies between the nearest neighbors for the…
A ``ballistic-search'' algorithm is presented which allows the identification of clusters (or funnels) of ground states in Ising spin glasses even for moderate system sizes. The clusters are defined to be sets of states, which are connected…
We investigate slow non-equilibrium dynamical processes in two-dimensional $q$--state Potts model with both ferromagnetic and $\pm J$ couplings. Dynamical properties are characterized by means of the mean-flipping time distribution. This…
Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. Identifying…
We consider the low energy spectrum of spin-1/2 two-dimensional triangular lattice models subject to a ferromagnetic Heisenberg interaction and a three spin chiral interaction of variable strength. Initially, we consider quasi-one…
We propose a new type of state sum model for two-dimensional surfaces that takes into account topology and spin. The definition used - new to the literature - provides a rich class of extended models called spin models. Both examples and…