Introduction to statistical physics I Silvio R.A. Salinas. p. cm. -(Graduate texts in contemporary physics) IncJudes bibliographical references and index.

We study a model for anisotropic ferromagnetic quantum domain walls. The large degeneracy of the ground state in the extreme anisotropic (Ising) limit, associated with the translational invariance of the "kink center, " is lifted in the quantum system in a peculiar way. The critical point, at which the Hamiltonian is invariant under the quantum group U~[SU(2)j, is exactly determined by a cluster method. We also find the ground state wave function at the critical point. Some generalizations of these results for arbitrary spin and dimension are obtained.A simple model of a spin-S quantum Heisenberg ferromagnet with a domain wall is given by the spin Hamiltonian = -J P(S"'S"+s + S~S"+s) r, 6 ags"'S"'"h g S"'g S"', (1) r, cst t r EF rEFs.where 1 ) 0 and 6~J are exchange parameters, and r is a lattice vector, with a neighbor r + 6, on a d-dimensional cubic lattice of side L. The effective field h~0 represents the interactions of the spins with the boundary surfaces F+ (F ) with positive (negative) normal vectors. In one dimension, a fully isotropic (J = 6) spin-2 quantum

No abstract

We formulate the Ising model with competing interactions on a Cayley tree, in the infinitecoordination limit, as a two-dimensional nonlinear mapping. The phase diagram displays a Lifshitz point and many modulated phases. We perform calculations to show the existence of a complete devil's staircase at low temperatures. Also, we give strong numerical evidence for the existence of chaotic phases associated with strange attractors.

We obtain the phase diagram of a ferromagnetic mixed Ising system, consisting of spin--, and spin-5 variables, on a Bethe lattice of coordination number z, with nearest-neighbor exchange interactions and single-ion terms. The problem is formulated as a discrete nonlinear map. There is a tricritical point for S integer and z~5. In the infinite-coordination-number limit, we regain the results of an exact calculation for a Curie-Weiss version of the model.