Related papers: Ensemble inequivalence in random graphs
We investigate the phase diagram of a three-component system of particles on a one-dimensional filled lattice, or equivalently of a one-dimensional three-state Potts model, with reflection asymmetric mean field interactions. The three types…
In a spin chain governed by a local Hamiltonian, we consider a microcanonical ensemble in the middle of the energy spectrum and a contiguous subsystem whose length is a constant fraction of the system size. We prove that if the bandwidth of…
We describe in detail a mathematical framework in which statistical ensembles of hybrid classical-quantum systems can be properly described. We show how a maximum entropy principle can be applied to derive the microcanonical ensemble of…
We demonstrate that the multicanonical approach is not restricted to Monte Carlo simulations, but can also be applied to simulation techniques such as molecular dynamics, Langevin, and hybrid Monte Carlo algorithms. The effectiveness of the…
Velazquez and Curilef have proposed a methodology to extend Monte Carlo algorithms that are based on canonical ensemble. According to our previous study, their proposal allows us to overcome slow sampling problems in systems that undergo…
In complex systems such as spin systems and protein systems, conventional simulations in the canonical ensemble will get trapped in states of energy local minima. We employ the generalized-ensemble algorithms in order to overcome this…
Gas transport and other complex real-world challenges often require solving and controlling partial differential equations (PDEs) defined on graph structures, which typically demand substantial memory and computational resources. The Random…
The phenomenon of partial equivalence of statistical ensembles is illustrated by discussing two examples, the mean-field XY and the mean-field spherical model. The configurational parts of these systems exhibit partial equivalence of the…
We propose a new generalized-ensemble algorithm, which we refer to as the multicanonical-multioverlap algorithm. By utilizing a non-Boltzmann weight factor, this method realizes a random walk in the multi-dimensional, energy-overlap space…
Universal dimensionless quantities, such as Binder ratios and wrapping probabilities, play an important role in the study of critical phenomena. We study the finite-size scaling behavior of the wrapping probability for the Potts model in…
A systematic comparison is conducted for pairing properties of finite systems at nonzero temperature as predicted by the exact solutions of the pairing problem embedded in three principal statistical ensembles, as well as the unprojected…
Symmetry properties of the microcanonical entropy surface as a function of the energy and the order parameter are deduced from the invariance group of the Hamiltonian of the physical system. The consequences of these symmetries for 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…
We present the speedup from a novel parallel implementation of the multicanonical method on the example of a lattice gas in two and three dimensions. In this approach, all cores perform independent equilibrium runs with identical weights,…
The thermodynamics and microstructure of confined fluids with small particle number are best described using the canonical ensemble. However, practical calculations can usually only be performed in the grand-canonical ensemble, which can…
Mesoscopic spin ensembles coupled to a cavity offer the exciting prospect of observing complex nonclassical phenomena that pool the microscopic features from a few spins with those of macroscopic spin ensembles. Here, we demonstrate how the…
We consider a one-dimensional lattice system of unbounded, real-valued spins with arbitrary strong, quadratic, finite-range interaction. We show that the canonical ensemble (ce) satisfies a uniform logarithmic Sobolev inequality (LSI). The…
A Microcanonical Finite Site Ansatz in terms of quantities measurable in a Finite Lattice allows to extend phenomenological renormalization (the so called quotients method) to the microcanonical ensemble. The Ansatz is tested numerically in…
Here we investigate how local properties of particles in a thermal bath influence the thermodynamics of the bath. We utilize nanothermodynamics, based on two postulates: that small systems can be treated self-consistently by coupling to an…
We employ an extension of ergodic theory to the random setting to investigate the existence of random periodic solutions of random dynamical systems. Given that a random dynamical system has a dissipative structure, we proved that a random…