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arXiv:cond-mat/0212579

The specific heat of the rwo-dimensional +/-J Ising model

Hidetsugu Kitatani, Toshimasa Chino, Hideshi Ohya

Published Dec 24, 2002• 0 citations
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Abstract

The specific heat of the two-dimensional $\pm J$ Ising model has been investigated by the numerical transfer matrix method and Monte Carlo simulations from a new point of view. The region where a part of the specific heat takes the negative value has been investigated, which is characteristic of frustrated systems and reflects the non-trivial degeneracy of the ground state. The region mentioned above is found to be fairly large in the $p-T$ plane ($p$ is the concentration of the ferromagnetic bond and $T$ is the temperature). Moreover, it includes the Nishimori line. Namely, it includes a part of the paramagnetic-ferromagnetic phase boundary, on which the specific heat cannot diverge. The present result indicates that the specific heat does not diverge at least on a part of the paramagnetic-ferromagnetic phase boundary above the multicritical point, which is in conflict with previous results.

DOI
10.48550/arxiv.cond-mat/0212579

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The specific heat of the two-dimensional ±J\pm J±J Ising model has been investigated by the numerical transfer matrix method and Monte Carlo simulations from a new point of view. The region where a part of the specific heat takes the negative value has been investigated, which is characteristic of frustrated systems and reflects the non-trivial degeneracy of the ground state. The region mentioned above is found to be fairly large in the p−Tp-Tp−T plane (ppp is the concentration of the ferromagnetic bond and TTT is the temperature). Moreover, it includes the Nishimori line. Namely, it includes a part of the paramagnetic-ferromagnetic phase boundary, on which the specific heat cannot diverge. The present result indicates that the specific heat does not diverge at least on a part of the paramagnetic-ferromagnetic phase boundary above the multicritical point, which is in conflict with previous results.
The specific heat of the two-dimensional ±J Ising model has been investigated by the numerical transfer matrix method and Monte Carlo simulations from a new point of view. The region where a part of the specific heat takes a negative value has been investigated, which is characteristic of frustrated systems and reflects the non-trivial degeneracy of the ground state. The region mentioned above is found to be fairly large in the p – T plane ( p is the concentration of the ferromagnetic bond and T is the temperature). Moreover, it includes the Nishimori line. Namely, it includes a part of the paramagnetic–ferromagnetic phase boundary, on which the specific heat cannot diverge. The present result indicates that the specific heat does not diverge at least on a part of the paramagnetic–ferromagnetic phase boundary above the multicritical point, which is in conflict with previous results.
The value of the critical exponent ν of the two-dimensional ± J Ising model along the ferromagnetic-nonferromagnetic phase boundary in the p - T plane ( p is the concentration of + J bonds; T is the temperature) has been calculated by the use of the transfer matrix method and the Roomany-Wyld approximation for long strips with finite width ( L ×10 5 : L ≤18), and has been found to take almost constant value, 1.0, at temperature above the Nishimori line. By the same method, a lower bound of the critical concentration between paramagnetic phase and the random antiphase state (RAS phase) has been calculated at some temperature below the Nishimori line in the p - T plane.
The two-dimensional (2D) random-bond Ising model has a novel multicritical point on the ferromagnetic to paramagnetic phase boundary. This random phase transition is one of the simplest examples of a 2D critical point occurring at both finite temperatures and disorder strength. We study the associated critical properties, by mapping the random 2D Ising model onto a network model. The model closely resembles network models of quantum Hall plateau transitions, but has different symmetries. Numerical transfer matrix calculations enable us to obtain estimates for the critical exponents at the random Ising phase transition. The values are consistent with recent estimates obtained from high-temperature series.
The ferromagnetic-nonferromagnetic phase boundary on the two-dimensional ± J Ising model in the p - T plane is determined by the use of the coherent-anomaly method (CAM) proposed by Suzuki, where p is the concentration of the + J bond, and T the temperature. The phase boundary below the Nishimori line has been found to be vertical at p =0.884±0.001 to the p -axis, which is consistent with the previous results obtained under the assumption of Suzuki's weak universality. The critical exponent γ p ( T ) has also been determined along the phase boundary, which shows a crossover tendency.