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On the Distribution and Gap Structure of Lee-Yang Zeros for the Ising Model: Periodic and Aperiodic Couplings

By João C.A. Barata, Jo~ao C. A. Barata and Pedro S. Goldbaum

Abstract

. In this work, we present some results on the distribution of Lee-Yang zeros for the ferromagnetic Ising model on the rooted Cayley Tree (Bethe Lattice), assuming free boundary conditions, and in the one-dimensional lattice with periodic boundary conditions. In the case of the Cayley Tree, we derive the conditions that the interactions between spins must obey in order to ensure existence or absence of phase transition at nite temperature (T 6= 0). The results are rst obtained for periodic interactions along the generations of the lattice. Then, using periodic approximants, we are also able to obtain results for aperiodic sequences generated by substitution rules acting on a nite alphabet. The particular examples of the Fibonacci and the Thue-Morse sequences are discussed. Most of the results are obtained for a Cayley Tree with arbitrary order d. We will be concerned in showing whether or not the zeros become dense in the whole unit circle of the fugacity variable. Regarding the one..

Year: 2007
OAI identifier: oai:CiteSeerX.psu:10.1.1.32.6232
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