Related papers: Exploring first-order phase transitions with popul…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
We present results for a variety of Monte Carlo annealing approaches, both classical and quantum, benchmarked against one another for the textbook optimization exercise of a simple one-dimensional double-well. In classical (thermal)…
A Monte Carlo algorithm is proposed to simulate ferromagnetic q-state Potts model for any real q>0. A single update is a random sequence of disordering and deterministic moves, one for each link of the lattice. A disordering move attributes…
Annealing algorithms such as simulated annealing and population annealing are widely used both for sampling the Gibbs distribution and solving optimization problems (i.e. finding ground states). For both statistical mechanics and…
The critical behaviour in short time dynamics for the q=6 and 7 state Potts models in two-dimensions is investigated. It is shown that dynamic finite-size scaling exists for first-order phase transitions.
One-dimensional model of a system where first-order phase transition occurs is examined in the present paper. It is shown that basic properties of the phenomenon, such as a well defined temperature of transition, are caused both by…
Parallel Quantum Annealing is a technique to solve multiple optimization problems simultaneously. Parallel quantum annealing aims to optimize the utilization of available qubits on a quantum topology by addressing multiple independent…
Evolutionary systems must learn to generalize, often extrapolating from a limited set of selective conditions to anticipate future environmental changes. The mechanisms enabling such generalization remain poorly understood, despite their…
We compare the transition barrier that accompanies a first-order phase transition in the canonical and microcanonical ensemble. This is directly encoded in the probability distributions of standard Metropolis Monte Carlo simulations and a…
A hybrid Potts model where a random concentration $p$ of the spins assume $q_0$ states and a random concentration $1-p$ of the spins assume $q>q_0$ states is introduced. It is known that when the system is homogeneous, with an integer spin…
Recently, Velazquez and Curilef have proposed a methodology to extend Monte Carlo algorithms based on canonical ensemble, which is aimed to overcome slow sampling problems associated with temperature-driven discontinuous phase transitions.…
Relying on the recently proposed multicanonical algorithm, we present a numerical simulation of the first order phase transition in the 2d 10-state Potts model on lattices up to sizes $100\times100$. It is demonstrated that the new…
We consider the ferromagnetic large-$q$ state Potts model in complex evolving networks, which is equivalent to an optimal cooperation problem, in which the agents try to optimize the total sum of pair cooperation benefits and the supports…
Population protocols are a distributed computation model in which a collection of anonymous, finite-state agents interact in randomly chosen pairs and update their states according to a fixed transition function. The computation is defined…
The random field Ising model with Gaussian disorder is studied using a new Monte Carlo algorithm. The algorithm combines the advantanges of the replica exchange method and the two-replica cluster method and is much more efficient than the…
We solve the mean-field-like $p$-spin Ising model under a spatio-temporal inhomogeneous transverse field to study the effects of inhomogeneity on the performance of quantum annealing. We find that the problematic first-order quantum phase…
In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target…
We present a new method for investigating first-order phase transitions using Monte Carlo simulations. It relies on the multiple-histogram method and uses solely histograms of individual phases. In addition, we extend the method to include…
We present a study of the phase diagram of a random optimization problem in presence of quantum fluctuations. Our main result is the characterization of the nature of the phase transition, which we find to be a first-order quantum phase…
We briefly review various computational methods for the solution of optimization problems. First, several classical methods such as Metropolis algorithm and simulated annealing are discussed. We continue with a description of quantum…