Tricritical point of the J_{1}J_{2} Ising model on a hyperbolic lattice
Abstract
The ferromagneticparamagnetic phase transition of the twodimensional frustrated Ising model on a hyperbolic lattice is investigated by use of the corner transfer matrix renormalization group method. The model contains a ferromagnetic nearestneighbor interaction J_{1} and a competing antiferromagnetic interaction J_{2} . A meanfieldlike secondorder phase transition is observed when the ratio κ=J_{2}/J_{1} is less than 0.203. In the region 0.203<κ<1/4 , the spontaneous magnetization is discontinuous at the transition temperature. Such tricritical behavior suggests that the phase transitions on hyperbolic lattices need not always be meanfieldlike.
 Publication:

Physical Review E
 Pub Date:
 December 2008
 DOI:
 10.1103/PhysRevE.78.061119
 arXiv:
 arXiv:0807.0150
 Bibcode:
 2008PhRvE..78f1119K
 Keywords:

 05.50.+q;
 05.70.Jk;
 64.60.F;
 75.10.Hk;
 Lattice theory and statistics;
 Critical point phenomena;
 Equilibrium properties near critical points critical exponents;
 Classical spin models;
 Condensed Matter  Statistical Mechanics
 EPrint:
 7 pages, 13 figures, submitted to Phys. Rev. E