Critical behavior at edge singularities in one dimensional spin models

Details Critical behavior at edge singularities in one dimensional spin models Critical behavior at edge singularities in one dimensional spin models

2008-09-26

arxiv.org/abs/0809.4510v1

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevE.78.031138

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

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