TY - JOUR
T1 - Ferromagnetic Potts models with multisite interaction
AU - Schreiber, Nir
AU - Cohen, Reuven
AU - Haber, Simi
N1 - Publisher Copyright:
© 2018 American Physical Society.
PY - 2018/3/8
Y1 - 2018/3/8
N2 - We study the q-state Potts model with four-site interaction on a square lattice. Based on the asymptotic behavior of lattice animals, it is argued that when q≤4 the system exhibits a second-order phase transition and when q>4 the transition is first order. The q=4 model is borderline. We find 1/lnq to be an upper bound on Tc, the exact critical temperature. Using a low-temperature expansion, we show that 1/(θlnq), where θ>1 is a q-dependent geometrical term, is an improved upper bound on Tc. In fact, our findings support Tc=1/(θlnq). This expression is used to estimate the finite correlation length in first-order transition systems. These results can be extended to other lattices. Our theoretical predictions are confirmed numerically by an extensive study of the four-site interaction model using the Wang-Landau entropic sampling method for q=3,4,5. In particular, the q=4 model shows an ambiguous finite-size pseudocritical behavior.
AB - We study the q-state Potts model with four-site interaction on a square lattice. Based on the asymptotic behavior of lattice animals, it is argued that when q≤4 the system exhibits a second-order phase transition and when q>4 the transition is first order. The q=4 model is borderline. We find 1/lnq to be an upper bound on Tc, the exact critical temperature. Using a low-temperature expansion, we show that 1/(θlnq), where θ>1 is a q-dependent geometrical term, is an improved upper bound on Tc. In fact, our findings support Tc=1/(θlnq). This expression is used to estimate the finite correlation length in first-order transition systems. These results can be extended to other lattices. Our theoretical predictions are confirmed numerically by an extensive study of the four-site interaction model using the Wang-Landau entropic sampling method for q=3,4,5. In particular, the q=4 model shows an ambiguous finite-size pseudocritical behavior.
UR - http://www.scopus.com/inward/record.url?scp=85044187385&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.97.032106
DO - 10.1103/PhysRevE.97.032106
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C2 - 29776066
AN - SCOPUS:85044187385
SN - 2470-0045
VL - 97
JO - Physical Review E
JF - Physical Review E
IS - 3
M1 - 032106
ER -