Scaling functions for Tsallis non--extensive statistics

1999/06/23 by Rafael Salazar, R. Salazar, Raúl Toral +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #Complex Systems and Time Series Analysis #Statistical Mechanics and Entropy #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/9906350

4 pages (including 3 figures) LaTeX file. Submitted to Phys. Rev. Lett

arxiv created 1999/06/23 · arxiv updated 2016/08/31

Abstract

We study the one-dimensional Ising model with long-range interactions in the context of Tsallis non-extensive statistics by computing numerically the number of states with a given energy. We find that the internal energy, magnetization, entropy and free energy follow non-trivial scaling laws with the number of constituents N and temperature T. Each of the scaling functions for the internal energy, the magnetization and the free energy, adopts three different forms corresponding to q>1, q=1 and q<1, being q the non-extensivity parameter of Tsallis statistics.

Cited by

• Broad histogram method for multiparametric Hamiltonians

Related

• Non-extensive thermodynamics of 1D systems with long-range interaction
• One-dimensional long-range Ising model: two (almost) equivalent approximations
• Gibbs Measures for Long-Range Ising Models
• Ising Model Scaling Functions at Short Distance
• Constraint correlation functions of the one-dimensional Ising model in the scaling limit