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 $T_{BKT}$, 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.

8 pages, 5 figures

References in corpus (5)

• Metastable states, anomalous distributions and correlations in the HMF model
• Applications of the divergence theorem in Bayesian inference and MaxEnt
• Dynamical temperature study for classical planar spin systems
• Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions
• Finite-size corrections to scaling of the magnetization distribution in the $2d$ $XY$-model at zero temperature

Cited by in corpus (4)

• Single-particle velocity distributions of collisionless, steady-state plasmas must follow Superstatistics
• Temperature is not an observable in superstatistics
• Gradient and Hessian-Based Temperature Estimator in Lattice Gauge Theories: A Diagnostic Tool for Stability and Consistency in Numerical Simulations
• General method to perform Microcanonical Monte Carlo Simulations