English

Critical behavior at edge singularities in one dimensional spin models

Statistical Mechanics 2009-11-13 v1

Abstract

In ferromagnetic spin models above the critical temperature (T>TcrT > T_{cr}) the partition function zeros accumulate at complex values of the magnetic field (HEH_E) with a universal behavior for the density of zeros ρ(H)HHE\sg\rho (H) \sim | H - H_E |^{\sg}. The critical exponent \sg\sg is believed to be universal at each space dimension and it is related to the magnetic scaling exponent yhy_h via \sg=(dyh)/yh\sg = (d-y_h)/y_h. In two dimensions we have yh=12/5(\sg=1/6)y_h=12/5 (\sg = -1/6) while yh=2(\sg=1/2)y_h=2 (\sg=-1/2) in d=1d=1. For the one dimensional Blume-Capel and Blume-Emery-Griffiths models we show here, for different temperatures, that a new value yh=3(\sg=2/3)y_h=3 (\sg =-2/3) can emerge if we have a triple degeneracy of the transfer matrix eigenvalues.

Keywords

Cite

@article{arxiv.0809.4510,
  title  = {Critical behavior at edge singularities in one dimensional spin models},
  author = {D. Dalmazi and F. L. Sá},
  journal= {arXiv preprint arXiv:0809.4510},
  year   = {2009}
}

Comments

to appear in Phys. Rev. E, 16 pages, 3 figures

R2 v1 2026-06-21T11:24:21.170Z