Related papers: Equilibrium Microcanonical Annealing for First-Ord…
Population annealing is a hybrid of sequential and Markov chain Monte Carlo methods geared towards the efficient parallel simulation of systems with complex free-energy landscapes. Systems with first-order phase transitions are among the…
A generalization of the microcanonical ensemble suggests a simple strategy for the simulation of first order phase transitions. At variance with flat-histogram methods, there is no iterative parameters optimization, nor long waits for…
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…
Two examples of Microcanonical Potts models, 2-dimensional nearest neighbor and mean field, are considered via exact enumeration of states and analytical asymptotic methods. In the interval of energies corresponding to a first order phase…
Phase transitions of first and second order can easily be distinguished in small systems in the microcanonical ensemble. Configurations of phase coexistence, which are suppressed in the canonical formulation, carry important information…
The numerical simulation of strongly first-order phase transitions has remained a notoriously difficult problem even for classical systems due to the exponentially suppressed (thermal) equilibration in the vicinity of such a transition. In…
The Potts model is a generalization of the Ising model with $Q>2$ components. In the fully connected ferromagnetic Potts model, a first-order phase transition is induced by varying thermal fluctuations. Therefore, the computational time…
The development of new algorithms for simulations in physics is as important as the development of new analytical methods. In this paper, we present a comparison of the recently developed microcanonical population annealing (MCPA) algorithm…
A microcanonical first order transition, connecting a clustered to a homogeneous phase, is studied from both the thermodynamic and dynamical point of view for a N-body Hamiltonian system with infinite-range couplings. In the microcanonical…
Using large-scale numerical simulations we studied the kinetics of the 2d q-Potts model for q > 4 after a shallow subcritical quench from a high-temperature homogeneous configuration. This protocol drives the system across a first-order…
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…
We implemented a parallel version of the multicanonical algorithm and applied it to a variety of systems with phase transitions of first and second order. The parallelization relies on independent equilibrium simulations that only…
We consider a Hamiltonian system made of $N$ classical particles moving in two dimensions, coupled via an {\it infinite-range interaction} gauged by a parameter $A$. This system shows a low energy phase with most of the particles trapped in…
An algorithm for Monte Carlo simulations is proposed in which the parameter controlling the strength of the transition becomes a dynamical variable and in which efficient transitions are achieved by cluster steps. It allows to avoid the…
Aggregation transitions in disordered mesoscopic systems play an important role in several areas of knowledge, from materials science to biology. The lack of a thermodynamic limit in systems that are intrinsically finite makes the…
The investigation of phase coexistence in systems with multi-component order parameters in finite systems is discussed, and as a generic example, Monte Carlo simulations of the two-dimensional q-state Potts model (q=30) on LxL square…
By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…
Algorithms for simulating complex physical systems or solving difficult optimization problems often resort to an annealing process. Rather than simulating the system at the temperature of interest, an annealing algorithm starts at a…
We present a novel framework exploiting the cascade of phase transitions occurring during a simulated annealing of the Expectation-Maximisation algorithm to cluster datasets with multi-scale structures. Using the weighted local covariance,…
We apply the Hierarchical Autoregressive Neural (HAN) network sampling algorithm to the two-dimensional $Q$-state Potts model and perform simulations around the phase transition at $Q=12$. We quantify the performance of the approach in the…