Potts model on infinitely ramified Sierpinski-gasket-type fractals and algebraic order at antiferromagnetic phases

First- and second-order quantum phase transitions of a q-state Potts model in fractal lattices

Quantum phase transitions of a q-state Potts model in fractal lattices are studied using a continuous-time quantum Monte Carlo simulation technique. For small values of q, the transition is found to be second order and critical exponents of the quantum critical point are calculated. The dynamic critical exponent z is found to be greater than one for all fractals studied, which is in contrast to integer-dimensional regular lattices. When q is greater than a certain value q_{c}, the phase transition becomes first order, where q_{c} depends on the lattice. Further analysis shows that the characteristics of phase transitions are more sensitive to the average number of nearest neighbors than the Hausdorff dimension or the order of ramification.

Ground-state entropies of the Potts antiferromagnet on diamond hierarchical lattices

The ground-state degeneracies of the q-state Potts antiferromagnet on general diamond hierarchical lattices are computed, for q> or =3, by means of two distinct methods. The first method, denominated the recursive approach, is based on exact recursion relations for the total number of ground states, leading to the exact ground-state entropy in the thermodynamic limit. The second method, called the factorization approach, consists in a simple approximation, where the total number of ground states is factorized as a product of the number of ground states at each hierarchy level. The factorization approach appears to be a poor approximation for small values of q, but its accuracy improves substantially as q increases, and it becomes exact in the limit q--> infinity. In spite of the fact that such a model presents no frustration, a residual entropy at zero temperature is found for all q> or =3. Similarly to what happens on Bravais lattices, the residual entropy approaches its maximum allowed value, ln q, as q increases.