Critical behaviour of a heat capacity for three-dimensional Ising model

George Allen Baker Jr., Rajan Gupta

Emilio N. M. Cirillo, Giuseppe Gonnella, Alessandro Pelizzola

V. I. Egorov, Olga G. Maksimova, Boris Kryzhanovsky +1 more

We investigated the behavior of a heat capacity near the critical temperature for the three-dimensional Ising model on a cubic lattice with the linear lattice size ranging from 10 to 256. The calculations were carried out by Metropolis and Wang-Landau algorithms. We find that the results obtained by both methods have a good agreement and they justify that the heat capacity has an infinite singularity at the critical point.

Igor A. Stepanov

Earlier, the isochoric heat capacity of the cubic lattice for the Ising model was calculated approximately. In the present paper, using the exact solution of the three-dimensional Ising model, this heat capacity is calculated exactly.

Hiroshi Katrumori

Yogendra P. Valani

Our aim is to investigate the critical behaviour of lattice spin models such as the three-dimensional Ising model in the thermodynamic limit. The exact partition functions (typically summed over the order of 1075 states) for finite simple cubic Ising lattices are computed using a transfer matrix approach. Q-state Potts model partition functions on two- and three-dimensional lattices are also computed and analysed. Our results are analysed as distributions of zeros of the partition function in the complex-temperature plane. We then look at sequences of such distributions for sequences of lattices approaching the thermodynamic limit. For a controlled comparison, we show how a sequence of zero distributions for finite 2d Ising lattices tends to Onsager’s thermodynamic solution. Via such comparisons, we find evidence to suggest, for example, a thermodynamic limit singular point in the behaviour of the specific heat of the 3d Ising model.