Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-06-25
Phys.Rev. E67 (2003) 066108
Physics
Condensed Matter
Statistical Mechanics
16 pages, 2 figures. Third version: the title was slightly changed. To be published in Physical Review E
Scientific paper
10.1103/PhysRevE.67.066108
We present both analytic and numerical results on the position of the partition function zeros on the complex magnetic field plane of the $q=2$ (Ising) and $q=3$ states Potts model defined on $\phi^3 $ Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs. For the $q=3$ states Potts model our perturbative results indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic results are confirmed by finite lattice numerical calculations.
Dalmazi D.
de Albuquerque Luiz C.
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