Absence of re-entrant phase transition of the antiferromagnetic Ising model on the simple c.pdf

a r X i v : c o n d - m a t / 9 4 0 9 0 9 3 v 1 2 2 S e p 1 9 9 4 Absence of re-entrant phase transition of the antiferromagnetic Ising model on the simple cubic lattice: Monte Carlo study of the hard- sphere lattice gas Atsushi Yamagata Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro- ku, Tokyo 152, Japan Running title Absence of re-entrant phase transition of antiferromagnetic Ising model Keywords Antiferromagnetic Ising model, Hard-sphere lattice gas, Monte Carlo method PACS classification codes 02.70.Lq, 05.50.+q, 64.60.Cn, 75.10.Hk Abstract We perform the Monte Carlo simulations of the hard-sphere lattice gas on the simple cubic lattice with nearest neighbour exclusion. The critical activity is estimated, zc = 1.0588± 0.0003. Using a relation between the hard-sphere lattice gas and the antiferromagnetic Ising model in an external magnetic field, we conclude that there is no re-entrant phase transition of the latter on the simple cubic lattice. 1 Introduction The antiferromagnetic Ising model shows a phase transition in an external magnetic field but the ferromagnetic one has a critical point only in zero field. The critical line surrounds the antiferromagnetic ordered phase [1, 2]. A Hamiltonian is H = |J |∑ 〈ij〉 si sj ?H ∑ i si, where si is an Ising spin variable located ith lattice site and which takes on the value +1 and ?1. The first summation is over all nearest neighbour pairs on a lattice and the second over all lattice sites. J( 0) is the exchange interaction. H is an external magnetic field. Many authors have studied the system by various methods: Bethe approximation [3], mean field approxi- mation [4], constant coupling approximation [5], Kikuchi approximation [6], series expansions [7, 8], Monte Carlo simulations [9, 10, 11, 12, 13, 14], trans- fer matrix [14], renormalization group with periodic cell clusters [15, 16] phenomenological renormalization group and transfer matrix [17, 18], exact calculations of an interfaci