Critical behavior at edge singularities in one dimensional spin models

Abstract

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 $ρ(H) \sim | H - H_E |^{\sg}$. 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.

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

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• Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism
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Cited by in corpus (1)

• Unusual Yang-Lee edge singularity in the one-dimensional axial-next-to-nearest-neighbor Ising model