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Journal of the Physical Society of Japan

Tricritical Behavior of an Ising Antiferromagnet with Next-Nearest Neighbor Ferromagnetic Interaction

Chikao Kawabata, Jos Rogiers, G. F. Tuthill, Eugene Stanley

Published Mar 1, 1977• 0 citations
Publisher

Abstract

Using high temperature series expansions, we have studied an Ising model with nearest-neighbor antiferromagnetic interaction ( J 1 <0) and next nearest neighbor ferromagnetic interaction ( J 2 >0), which is thought to exhibit a tricritical point (TCP). Assuming that tricritical exponents are mean-field like, we locate TCPs for several values of the exchange coupling parameter J 2 / J 1 by the method of log-Padé analysis.

DOI
10.1143/jpsj.42.1055

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Using high temperature series expansions, we have studied an Ising model with nearest-neighbor antiferromagnetic interaction ( J 1 <0) and next nearest neighbor ferromagnetic interaction ( J 2 >0), which is thought to exhibit a tricritical point (TCP). Assuming that tricritical exponents are mean-field like, we locate TCPs for several values of the exchange coupling parameter J 2 / J 1 by the method of log-Padé analysis.
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The nnn model is an Ising model with nearest-neighbor antiferromagnetic interactions (J1<0{J}_{1}<0J1​<0) but also next-nearest-neighbor ferromagnetic exchange (J2>0{J}_{2}>0J2​>0). This model is analyzed in external magnetic field using the same techniques as applied to the meta model of Paper I. Again, the staggered susceptibility ${\ensuremath{\chi}}_{\mathrm{st}}$ appears to diverge along the critical line in the $H\ensuremath{-}T$ plane with a constant exponent ${\ensuremath{\gamma}}_{\mathrm{st}}=\frac{5}{4}$, consistent with the universality hypothesis. However, in contrast to the meta model, it is found that the direct susceptibility $\ensuremath{\chi}$ diverges at the tricritical point with an exponent $\overline{\ensuremath{\gamma}}\ensuremath{\simeq}\frac{1}{4}$. Implications of the scaling hypothesis at the tricritical point are discussed and the results for both the meta and nnn models are utilized to obtain the scaling power a‾2{\overline{a}}_{2}a2​ corresponding to the "weak" direction (in the sense of Griffiths and Wheeler). Included in this discussion is the double-power-law form, predicted to hold within the crossover region by tricritical-point scaling.
The authors study the Ising model on the triangular lattice with nearest-neighbor couplings K(nn) , next-nearest-neighbor couplings K(nnn) >0 , and a magnetic field H . This work is done by means of finite-size scaling of numerical results of transfer matrix calculations, and Monte Carlo simulations. We determine the phase diagram and confirm the character of the critical manifolds. The emphasis of this work is on the antiferromagnetic case K(nn) <0 , but we also explore the ferromagnetic regime K(nn) >/=0 for H=0 . For K(nn) <0 and H=0 we locate a critical phase presumably covering the whole range -infinity< K(nn) <0 . For K(nn) <0 , H not equal 0 we locate a plane of phase transitions containing a line of tricritical three-state Potts transitions. In the limit H-->infinity this line leads to a tricritical model of hard hexagons with an attractive next-nearest-neighbor potential.
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