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Communications in Theoretical Physics

Critical Behavior of an NNN Interaction Model

Hai-Yan Zhang, Bo-Wei Xu

Published Jul 1, 1992• 0 citations
Publisher

Abstract

A one-dimensional quantum mode1 with generalized next-nearest neighbour interaction is studied. The numerical results convince us of the existence of critical phenomenon in this model. The critical point condition is given, and the model belongs to the Ising universality.
DOI
10.1088/0253-6102/18/1/1

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The critical behaviour of the Ising model on the square lattice with ferromagnetic nearest-neighbour interactions (J) and anti-ferromagnetic next-nearest neighbour interactions (J') is discussed for small lambda =J/ mod J' mod . The singular part of the free energy is calculated to second order in lambda by perturbation theory. Near the critical temperature of the unperturbed system (J=0), this expansion is found to have a form which may be exponentiated yielding, for non-zero lambda , a non-universal critical line along which the exponents vary continuously with lambda . For small lambda , the specific heat exponent, alpha = alpha 1 lambda 2 +O( lambda 2 ) with alpha 1 approximately=1.5.