Thermodynamic Limit for a Spin Lattice

Didier Arnal, J. C. Cortet

C.-A. Piguet, D. F. Wang, C. Gruber

In this work, a multichannel Kondo lattice model is studied in the thermodynamic limit. The conduction band is described by a constant hopping amplitude between any pair of lattice sites. For this system, we have obtained the exact thermodynamical properties and the ground state energies. In the limit of strong interaction between the electrons and the impurity spins, the wavefunctions take the Jastrow product form.

Masanori Ohya, Dėnes Petz

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.

A. L. Lewis

Recent lattice-renormalization-group calculations have investigated the effect of placing arbitrarily large numbers of spins into blocks, via Monte Carlo numerical methods. These calculations indicate that, in the thermodynamic limit, the fixed point of the recursion relation converges to the exact critical temperature, even though the recursion relations themselves become nonanalytic. It is the purpose of this note to explain why this occurs.

Nick G. Duffield