We present a comparative study of the effects of random and aperiodically distributed interactions on the critical behavior of a model for two interacting polymers on a diamond hierarchical lattice. The problem is formulated in terms of exact renormalization-group (RG) recursion relations. In...

We write the exact renormalization-group recursion relations for nearest-neighbor ferromagnetic Ising models on Migdal–Kadanoff hierarchical lattices with a distribution of aperiodic exchange interactions according to a class of substitutional sequences. For small geometric fluctuations, the...

We present some calculations for the thermodynamic behavior of mean-field ferromagnetic p-spin interaction models in the presence of quenched random fields. For both Ising and spherical spin variables, we use the law of large numbers, without recourse to the replica trick, to obtain a...

We investigate the phase diagram of a spin-1/2 Ising model on a cubic lattice, with competing interactions between nearest and next-nearest neighbors along an axial direction, and fully connected spins on the sites of each perpendicular layer. The problem is formulated in terms of a set of...

The critical behavior of magnetic model systems in the mean-field approximation may be obtained from a standard Landau expansion, in terms of the order parameter m, of the functional ψ(T,H; m) = −Hm + f(T,m), where f is the Helmholtz free energy. As an alternative procedure, the Gibbs free...

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T, a quantum parameter g, and the ratio p=−J2/J1, where J10 refers to ferromagnetic interactions between first-neighbour sites along the d directions of a hypercubic lattice, and J2<0 is associated with competing antiferromagnetic interactions between second neighbours along m≤d directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g=0 space, with a Lifshitz point at p=1/4, for d>2, and closed-form...</0>

We propose two schemes to construct aperiodic spin models on hierarchical lattices. As in previous works, we choose nearest-neighbor exchange interactions according to a substitution rule. In contrast to these works, however, we are able to deal with Thue–Morse substitutions, a→ab, b→ba,...

We include p-spin interactions in a spherical version of a soluble mean-field spin-glass model proposed by van Hemmen. Due to the simplicity of the solutions, which do not require the use of the replica trick, we are able to carry out a detailed investigation of a number of special situations....

We investigate the effects of the inclusion of aperiodic interactions in the Ising chain with competing ferro and antiferromagnetic couplings between nearest and next-nearest-neighbor sites. In particular, we obtain the exact ground state, including the spin arrangements and the residual...

We use real- and momentum-space renormalization-group techniques to obtain the phase diagram of a mixed-spin Ising model (spin-12 and spin-1) in the presence of a crystal field. A detailed analysis of the fixed points and the flow diagrams of the Migdal-Kadanoff real-space renormalization-group...