Thermodynamic calculation of spin scaling functions

2018/08/23 by Ruppeiner, George
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.1808.07933

Abstract

Critical phenomena theory centers on the scaled thermodynamic potential per spin ϕ(β, h)=|t|^pY(h|t|^-q), with inverse temperature β=1/T, h=-βH, ordering field H, reduced temperature t=t(β), critical exponents p and q, and function Y(z) of z=h|t|^-q. I discuss calculating Y(z) with the information geometry of thermodynamics. Scaled solutions obtain with three admissible functions t(β): 1) t=e^-Jβ, 2) t=β^-1, and 3) t=β_C-β, where J and β_C are constants. For p=q, information geometry yields Y(z)=√(1+z²), consistent with the one-dimensional (1D) ferromagnetic Ising model.

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