Ensemble-free configurational temperature for spin systems

Abstract

An estimator for the dynamical temperature in an arbitrary ensemble is derived in the framework of Bayesian statistical mechanics and the maximum entropy principle. We test this estimator numerically by a simulation of the two-dimensional XY-model in the canonical ensemble. As this model is critical in the whole region of temperatures below the Berezinski-Kosterlitz-Thouless critical temperature TBKT , we use a generalization of Wolff's uni-cluster algorithm. The numerical results allow us to confirm the robustness of the analytical expression for the microscopic estimator of the temperature. This microscopic estimator has also the advantage that it gives a direct measure of the thermalization process and can be used to compute absolute errors associated to statistical fluctuations. In consequence, this estimator allows for a direct, absolute and astringent test of the ergodicity of the underlying Markov process, which encodes the algorithm used in a numerical simulation.

Single-particle velocity distributions of collisionless, steady-state plasmas must follow superstatistics

“…On the other hand, applying the conjugate variables theorem [16] to the distribution P (Γ|S) = p(H(Γ)) and using the chain rule for the gradient of ln P (Γ|S), we see that [17] ∇…”

Emergence of Tsallis statistics as a consequence of invariance

“…1. Now the generalized Boltzmann factor ρ(E) is (12) and the fundamental inverse temperature is given by [16]…”

“…A model with fundamental inverse temperature β F has a generalized equipartition theorem given by [12]…”

“…For a steady state described by Eq. 7, let us define the fundamental inverse temperature function [11][12][13], denoted by β F (E), as the derivative…”

General method to sample systems in the microcanonical ensemble using Monte Carlo simulations

“…We will illustrate our method by simulating the well-known XY-model defined on a square lattice of lattice size L (see ref. [15] for an accurate analysis of the configurational temperature for this model). The Hamiltonian for this model is: H = −JS 2 ∑ <i, j> cos (θ i − θ j ), being J > 0 the ferromagnetic coupling constant, θ i is the angle of the spin magnetic moment of magnitude S relative to some direction at the i-th lattice site.…”