We study a modification of the Evolutionary Minority Game (EMG) in which agents are placed in the nodes of a regular or a random graph. A neighborhood for each agent can thus be defined and a modification of the usual relaxation dynamics can be made in which each agent updates her decision...

We review and extend some recent investigations of the effects of aperiodic interactions on the critical behavior of ferromagnetic q-state Potts models. By considering suitable diamond or necklace hierarchical lattices, and assuming a distribution of interactions according to a class of...

The paper discusses the transformation of decorated Ising models into an effective undecorated spin model, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The inverse of a Vandermonde matrix with equidistant nodes [−s,s] is...

Through Monte Carlo Simulation, the well-known majority-vote model has been studied with noise on directed random graphs. In order to characterize completely the observed order–disorder phase transition, the critical noise parameter qc, as well as the critical exponents β/ν, γ/ν and 1/ν...

We simulate the kinetic Ashkin-Teller model with both ordered and disordered initial states, evolving in contact with a heat-bath at the critical temperature. The power-law scaling behaviour for the magnetic order and electric order are observed in the early time stage. The values of the...

The q-state Potts antiferromagnet exhibits nonzero ground state entropy S0({G},q)≠0 for sufficiently large q on a given n-vertex lattice Λ or graph G and its n→∞ limit {G}. We present exact calculations of the zero-temperature partition function Z(G,q,T=0) and W({G},q), where S0=kBlnW,...

The lattice spin model with Q-component discrete spin variables restricted to have orientations orthogonal to the faces of Q-dimensional hypercube is considered on the Bethe lattice, the recursive graph which contains no cycles. The partition function of the model with dipole–dipole and...

The partition function (Fisher) zeros of the Q-state Potts model with three-site interactions on a zigzag ladder are studied by a transfer-matrix approach. This Q-state model is proposed as a description of helix-coil transition in homopolymers. The Fisher zeros are exactly derived for arbitrary...

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 study the Damage Spreading on the two-dimensional ferromagnetic q-state Potts model using Swendsen–Wang dynamics. We find two damage spreading transitions: damage does not spread either at low or high temperatures. At the transition occurring near the Curie temperature our numerical results...