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Physics Letters A

Sublattice magnetizations in non-zero magnetic field in an antiferromagnetic infinite-range Ising model

Andrés Ayuela, Douglas J. Klein, Norman Henry March

Published Jul 4, 2006• 1 citation
Publisher
DOI
10.1016/j.physleta.2006.06.057

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A new one-dimensional antiferromagnetic Ising model with exponential pair interactions is proposed. This model is composed of 2N Ising spins, half of which belong to an α-sublattice and the others to a β-sublattice. The interaction between spins in the same sublattice is long-rang ferromagnetic and that between spins in the different sublattices is long-rang antiferromagnetic. Thermodynamic properties of the model are shown to be the same as those obtained by using the molecular field theory for the Ising model with nearest-neighbor interactions.
We study classical Ising spin-1/2 models on a two-dimensional (2D) square lattice with ferromagnetic or antiferromagnetic nearest-neighbor interactions, under the effect of a pure imaginary magnetic field. The complex Boltzmann weights of spin configurations cannot be interpreted as a probability distribution, which prevents application of standard statistical algorithms. In this work, the mapping of the Ising spin models under consideration onto symmetric vertex models leads to real (positive or negative) Boltzmann weights. This enables us to apply accurate numerical methods based on the renormalization of the density matrix, namely, the corner transfer matrix renormalization group and the higher-order tensor renormalization group. For the 2D antiferromagnet, varying the imaginary magnetic field, we calculate with high accuracy the curve of critical points related to the symmetry breaking of magnetizations on the interwoven sublattices. The critical exponent β and the anomaly number c are shown to be constant along the critical line, equal to their values β=1/8 and c=1/2 for the 2D Ising model in a zero magnetic field. The 2D ferromagnets behave in analogy with their 1D counterparts defined on a chain of sites, namely, there exists a transient temperature which splits the temperature range into its high-temperature and low-temperature parts. The free energy and the magnetization are well defined in the high-temperature region. In the low-temperature region, the free energy exhibits singularities at the Yang-Lee zeros of the partition function and the magnetization is also ill-defined: It varies chaotically with the size of the system. The transient temperature is determined as a function of the imaginary magnetic field by using the fact that from the high-temperature side both the first derivative of the free energy with respect to the temperature and the magnetization diverge at this temperature.