We consider two distinct ways of introducing elastic degrees of freedom in the one-dimensional Ising model. Taking into account the average effect of elastic vibrations, the effective spin Hamiltonian in the pressure ensemble diplays long-rang interactions which give rise to a first-order phase transition. However, local fluctuation of the crystalline positions lead to an effective spin Hamiltonian with short-range interactions and without any thermodynamic anomaly in one dimension.

Semina Ciências Exatas e TecnológicasDec 15, 19890 citations

Computer Physics Communications

The effect of vibrational degrees of freedom on the phase transition in the 2D Ising model

S.V. Stroganova, Mikhail I. Vasilevskiy, Olga V. Vikhrova

Published Sep 1, 1999• 0 citations

Publisher

DOI: 10.1016/s0010-4655(06)70144-8

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XXZ

chains which, for example, can be a minimal model to describe the magnetic properties of compounds in which uranium and rare earth atoms form zig-zag chains. As with the Ising model for a certain set of parameters the model can undergo three phase transitions. However, both inchain and interchain plain interactions

s_{i,j}^x s_{k,l}^x+s_{i,j}^y s_{k,l}^y

can eliminate the reentrant disordered phase and then only one transition takes place. Additionally, the

XXZ

model can undergo temperature-induced metamagnetic transition.