Related papers: Efficient quantum and simulated annealing of Potts…
The $q$-state Potts chain with ferromagnetic couplings, $J=1$, in the presence of a transverse field, $\Gamma$, has a quantum phase transition at $\Gamma/q=1$, which is continuous for $q \le 4$ and of first order for $q>4$. Here we…
The one-dimensional (1D) $J_1$-$J_2$ $q$-state Potts model is solved exactly for arbitrary $q$ by analytically block-diagonalizing the original $q^2\times q^2$ transfer matrix into a simple $2\times 2$ maximally symmetric subspace, based on…
Traditional simulated annealing utilizes thermal fluctuations for convergence in optimization problems. Quantum tunneling provides a different mechanism for moving between states, with the potential for reduced time scales. We compare…
Despite the fact that a complete theoretical description of critical phenomena in connection with phase transitions has been well-established through the renormalization group theory, the microscopic nature of the phase transitions remains…
We propose a spinless Bose-Hubbard model in an one-dimensional (1D) double-chain tilted lattice at unit filling per cell. A subspace of this model can be faithfully mapped to the 1D transverse Ising model through superexchange interaction…
Low-temperature magnetization curves and thermodynamics of a frustrated spin-1/2 Heisenberg triangular bilayer with the antiferromagnetic intradimer interaction and either ferromagnetic or antiferromagnetic interdimer interaction are…
We study the q-state Potts model on the simple cubic lattice with ferromagnetic interactions in one lattice direction, and antiferromagnetic interactions in the two other directions. As the temperature T decreases, the system undergoes a…
In this paper, we review a way to change nature of phase transition with annealing methods in mind. Annealing methods are regarded as a general technique to solve optimization problems efficiently. In annealing methods, we introduce a…
We exhibit infinite families of two-dimensional lattices (some of which are triangulations or quadrangulations of the plane) on which the q-state Potts antiferromagnet has a finite-temperature phase transition at arbitrarily large values of…
For $d \ge 2$ and all $q\geq q_{0}(d)$ we give an efficient algorithm to approximately sample from the $q$-state ferromagnetic Potts and random cluster models on finite tori $(\mathbb Z / n \mathbb Z )^d$ for any inverse temperature…
The applicability of artificial neural networks (ANNs) is typically limited to the models they are trained with and little is known about their generalizability, which is a pressing issue in the practical application of trained ANNs to…
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 present the exact solution of the 1D classical short-range Potts model with invisible states. Besides the $q$ states of the ordinary Potts model, this possesses $r$ additional states which contribute to the entropy, but not to the…
Using the Wang-Landau Monte Carlo method, we study the antiferromagnetic (AF) three-state Potts model with a staggered polarization field on the square lattice. We obtain two phase transitions; one belongs to the ferromagnetic three-state…
We explore the Potts model on the generalized decorated square lattice, with both nearest (J1) and next-neighbor (J2) interactions. Using the tensor renormalization-group method augmented by higher-order singular value decompositions, we…
We propose a nonadiabatic approach to quantum annealing, in which we repeat quantum annealing in nonadiabatic time scales, and collect the final states of many realizations to find the ground state among them. In this way, we replace the…
We study the phase diagram of the ferromagnetic $q$-state Potts model on the various three-dimensional lattices for integer and non-integer values of $q>1$. Our approach is based on a thermodynamically self-consistent Ornstein-Zernike…
We study graphical representations for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960's. The second…
Generalizing the mapping between the Potts model with nearest neighbor interaction and six vertex model, we build a family of "fused Potts models" related to the spin $k/2$ ${\rm U}_{q}{\rm su}(2)$ invariant vertex model and quantum spin…
We study dynamic behavior of Potts model with invisible states near the first-order phase transition temperature. We focus on melting process starting from the perfect ordered state. This model is regarded as a standard model to analyze…