Journal of Physics A Mathematical and General

Series expansion study of first- and second-order phase transitions in a model with multispin coupling

Ferenc Iglói, D. Kapor, M. J. Škrinjaŕ, Jenő Sólyom

Published May 11, 1986• 22 citations

Abstract

The type of phase transition in a chain of Ising spins with multispin interaction is studied in a transverse field, using strong- and weak-coupling expansions. The transition is shown to be of first order if more than three spins are coupled. The critical exponents for the three-spin coupling model are estimated.

DOI: 10.1088/0305-4470/19/7/020

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Journal of Physics A Mathematical and General

Series expansion study of first- and second-order phase transitions in a model with multispin coupling

Ferenc Iglói, D. Kapor, M. J. Škrinjaŕ, Jenő Sólyom

Published May 11, 1986• 22 citations

Publisher

Abstract

DOI: 10.1088/0305-4470/19/7/020

Related papers

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Physical review. B, Condensed matterAug 1, 19813 citations

An Ising-type model including

n

-spin nearest-neighbor interactions is introduced. The ground-state properties of its Hamiltonian version are studied in one and two dimensions. The model is self-dual in one dimension. The mean-field theory indicates that for

n>{n}_{c}

the transition may become first order. Finite-size scaling suggests that

{n}_{c}=4

in one dimension. The critical exponents as functions of

n

are estimated.

The global phase diagram of the

S=1

Ising model in a transverse field is studied using a mean-field approximation. The critical behavior has also been considered by real-space renormalization-group techniques. This model is used to analyze the phase diagram of weakly coupled ($\frac{{J}_{\ensuremath{\perp}}}{{J}_{\ensuremath{\parallel}}}<<1$) classical Blume-Emery-Griffith chains. It is found that such systems display a first-order transition only in a very limited range of their parameters.

Recent lattice Hamiltonian strong-coupling calculations for the (1+1)-dimensional Ising, O(2), O(3), and O(4) models are extended to

d+1

dimensions and to general

\mathrm{O}(n)

symmetry. This allows a nontrivial numerical check on the rate of convergence of the strong-coupling expansions as the multidimensional models all have standard second-order phase transitions which have been well studied by other methods. Dlog-Pad\'e analysis of the fourth-order mass gap series for the (2+1)-dimensional Ising model show the critical exponent $\ensuremath{\nu}$ to be calculated to about the 10% level of accuracy. The behavior of $\ensuremath{\nu}$ as a function of

d

and

n

is exhibited and compared against known results. Mean-field behavior is recovered exactly in the $d\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, while the Berlin-Kac spherical model is obtained in the $n\ensuremath{\rightarrow}\ensuremath{\infty}$ limit.