Critical dynamics in d dimensions can be mapped onto a supersymmetric equilibrium problem in d+1 with a Lifshitz tricritical point. The existence of such a point is demonstrated for the Ising model on the hcp lattice by Monte Carlo simulation.

Physical review. B, Condensed matterSep 1, 198520 citations

Physica A Statistical Mechanics and its Applications

Critical temperature of the Ising ferromagnet on the fcc, hcp, and dhcp lattices

Unjong Yu

Published Oct 12, 2014• 13 citations

Publisher

DOI: 10.1016/j.physa.2014.10.001

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The susceptibility of simple-cubic-lattice ferromagnetic Ising films of

n

two-dimensional lattice layers is studied by extrapolation of high-temperature series expansions (to eleventh and twelfth orders) for

n=3,4,\dots{},14

layers with periodic boundary conditions, and

n=3,4,\dots{},10

layers with free-surface conditions. The corresponding surface susceptibility series for sc, bcc, and fcc lattices are analyzed in the light of universality hypotheses. On the basis of finite-size scaling theory explicit scaling functions are constructed describing the crossover from two-dimensional to three-dimensional critical behavior in terms of the ratio $\frac{n}{\ensuremath{\xi}(T)}$, where $\ensuremath{\xi}\ensuremath{\sim}\ensuremath{\Delta}{T}^{\ensuremath{-}\ensuremath{\nu}}$ is the bulk correlation length.

{\mathrm{x}}^{2}

is a slowly converging two dimensionally infinite sum. The resulting phase boundary coincides to order

{\mathrm{x}}^{2}

with the line onto which Domany mapped a two-dimensional kinetic Ising model. This lends support to the conjecture of Domany and Gubernatis that this special line coincides with the exact ferromagnetic phase boundary.