Critical exponents in mean-field classical spin systems

Yoshiyuki Y Yamaguchi; Debraj Das; Shamik Gupta

doi:10.1103/PhysRevE.100.032131

Critical exponents in mean-field classical spin systems

Phys Rev E. 2019 Sep;100(3-1):032131. doi: 10.1103/PhysRevE.100.032131.

Authors

Yoshiyuki Y Yamaguchi¹, Debraj Das², Shamik Gupta²

Affiliations

¹ Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
² Department of Physics, Ramakrishna Mission Vivekananda University, Belur Math, Howrah 711202, India.

PMID: 31640062
DOI: 10.1103/PhysRevE.100.032131

Abstract

For mean-field classical spin systems exhibiting a second-order phase transition in the stationary state, we obtain within the corresponding phase-space evolution according to the Vlasov equation the values of the critical exponents describing power-law behavior of response to a small external field. The exponent values so obtained significantly differ from the ones obtained on the basis of an analysis of the static phase-space distribution, with no reference to dynamics. This work serves as an illustration that cautions against relying on a static approach, with no reference to the dynamical evolution, to extract critical exponent values for mean-field systems.