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Modern Physics Letters B

CLUSTER VARIATION APPROACH TO THE ANTIFERROMAGNETIC TRANSITION OF THE t-J MODEL

Andrea Danani, Alessandro Pelizzola

Published Nov 20, 1993• 2 citations
Publisher

Abstract

The antiferromagnetic phase transition associated with the breaking of the magnetic SU(2) symmetry of the t-J model is investigated by means of the cluster variation method in the pair approximation. The disordered and antiferromagnetic phases are characterized by means of their symmetry properties, and an analytical implicit expression is given for the Néel temperature.

DOI
10.1142/s021798499300179x

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The antiferromagnetic phase transition associated with the breaking of the magnetic SU(2) symmetry of the t-J model is investigated by means of the cluster variation method in the pair approximation. The disordered and antiferromagnetic phases are characterized by means of their symmetry properties, and an analytical implicit expression is given for the Néel temperature.
Motivated by a recent proposal of a Bethe approximation for the triangular Ising antiferromagnet [Phys. Rev. B 56, 8241 (1997)], which seems to predict a disordered phase at any temperature in zero field, we analyze in some detail several mean-field-like approximations for this model, namely, the Bethe approximation itself, the cluster variation method, and the hard-spin mean-field theory. We show (i) that the disordered phase predicted by the Bethe approximation is unphysical at low enough temperature because of a negative entropy; (ii) how the results of the cluster variation method (namely, zero-temperature entropy and critical temperature of the spurious transition) converge to the exact ones for increasing cluster size; (iii) that it is possible to construct a cluster variation approximation which yields a disordered phase which is stable down to zero temperature; (iv) a few, so far unknown, zero-temperature results (entropy and internal energy) of the hard-spin mean-field theory.
Motivated by a recent proposal of a Bethe approximation for the triangular Ising antiferromagnet [Phys. Rev. B {\bf 56}, 8241 (1997)], which seems to predict a disordered phase at any temperature in zero field, we analyze in some detail several mean-field like approximations for this model, namely the Bethe approximation itself, the cluster variation method and the hard-spin mean-field theory. We show: (i) that the disordered phase predicted by the Bethe approximation is unphysical at low enough temperature because of a negative entropy; (ii) how the results of the cluster variation method (namely, zero temperature entropy and critical temperature of the spurious transition) converge to the exact ones for increasing cluster size; (iii) that it is possible to construct a cluster variation approximation which yields a disordered phase which is stable down to zero temperature; (iv) a few, so far unknown, zero temperature results (entropy and internal energy) of the hard-spin mean-field theory.
In this work we study the effects of quantum fluctuations in a disordered magnetic system. We consider a cluster-spin Ising model with antiferromagnetic short range interactions (J0) and disordered long range interactions (J) between clusters, where the system is under the influence of a transverse magnetic field Γ. The analytic treatment of the model is done by the replica method and Trotter formalism, in which a cluster mean field, replica symmetric and static approximations are used. This allows us to obtain an effective model of a single cluster that is exactly diagonalized. Thermodynamic quantities like order parameter and free energy are obtained then, the phase diagrams are analyzed. They are shown in temperature versus J0=J phase diagrams for some intensities of Γ. With Γ = 0, when we decrease the temperature (for lower intensities of J0=J) a continuous phase transition between the paramagnetic and cluster spin glass state (CSG) is found. When we increase the ratio J0=J, the system presents the antiferromagnetic phase (AF). The CSG state and the AF phase are separated by first order transitions. In the intermediate region of disorder, there exist a small interval in the AF-PM transition that is first order. When Γ is increased, the transitions PM-AF and PM-VSC decrease toward critical points in the lower and higher disorder, respectively. It is worth to note, in the intermediate range of disorder, that the transition CSG-AF disappears, letting a PM phase between them, even for zero temperature. Besides that, the first-order region, in the PM-AF transition, turns into a second order phase transition, changing its criticality in the low temperature regime. Our results show that quantum fluctuations affects the phase transitions of the model being capable to suppress and/or change his criticality. The present work suggests a model and a mechanism of the change in the criticality away from the quantum critical point, helping the investigation of this interesting and recent topic.
The three-state antiferromagnetic Potts model on the simple cubic lattice is studied by the Monte Carlo method using a new order parameter and employing the histogram technique. It is shown that apart from the low-temperature broken-sublattice-symmetry phase with nonequivalent sublattices, another type of ordering with equivalent sublattices does exist in the model between the broken-sublattice-symmetry and disordered phases. The temperature of the transition between the ordered phases is estimated from the histogram of the order parameter. The value obtained is in good agreement with that obtained from cluster variation circulations.
We investigate the phase diagram of the Heisenberg antiferromagnet on the square lattice with two different nearest-neighbour bonds J and J' ( J – J' model) at zero temperature. The model exhibits a quantum phase transition at a critical value between a semi-classically ordered Néel and a magnetically disordered quantum paramagnetic phase of valence-bond type, which is driven by local singlet formation on J' bonds. We study the influence of spin quantum number s on this phase transition by means of a variational mean-field approach, the coupled cluster method and the Lanczos exact-diagonalization technique. We present evidence that the critical value increases with growing s according to .