Erratum: Spin-1/2 Ising-Heisenberg model with the pairXYZHeisenberg interaction and quartic Ising interactions as the exactly soluble zero-field eight-vertex model [Phys. Rev. E79, 051103 (2009)

Abstract

We have recently realized that some particular results for critical exponents are erroneous in this paper. The critical exponents of the spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction and quartic Ising interactions were exactly calculated from a precise mapping correspondence with the critical exponents of the equivalent zero-field eight-vertex model, whereas the latter ones were expressed in terms of the parameter μ = 2 arctan(ω5ω7/ω1ω3) through the set of Eqs. (11). However, this is not in general correct unless the largest Boltzmann’s weight of the equivalent zero-field eight-vertex model is either ω5 or ω7. If either ω1 or ω3 represents the largest Boltzmann’s weight, then, one should consider the different expression for the parameter μ = 2 arctan(ω1ω3/ω5ω7) that determines the changes of critical exponents through the set of Eqs. (11) [1]. According to this, the critical exponents displayed in Figs. 6 and 7 for the model with the uniform quartic Ising interactions falling into the domain with the largest Boltzmann’s weight ω1 or ω3 lie in error. On the other hand, the critical exponents depicted in Figs. 8 and 9 for the model with the nonuniform quartic Ising interactions falling into the domain with the largest Boltzmann’s weight ω′ 5 or ω ′ 7 are correct. It is worthy to notice, moreover, that the effective Boltzmann’s weights of the uniform and nonuniform models are connected by means of the relations ω′ 1 = ω′ 3 = ω5, ω′ 5 = ω3 and ω′ 7 = ω1, and hence, it follows that both investigated particular cases in fact exhibit the identical behavior of both critical temperatures as well as critical exponents. Consequently, the erroneous results for the critical exponents shown in Figs. 6 and 7 can simply be replaced with the ones displayed in Figs. 8 and 9. It should be mentioned that this error has no effect on the other results presented in this paper apart from the conclusions we drew from Figs. 6 and 7 that need to be corrected. The critical exponent α for the specific heat is always non-negative, it continuously changes with the interaction parameters (as shown in Figs. 8 and 9) and the quantum critical point between the phases |I〉 and |II〉 (or |III〉 and |IV〉) is a discontinuous (first-order) phase transition rather than the unusual continuous phase transition of the infinite order.