Single-cluster Monte Carlo study of the Ising model on two-dimensional random lattices

Monte Carlo study of asymmetric 2D XY model

“…(24) and a power-law Ansatz with a small non-zero exponent ~. This is a well-known problem with fits of the specific heat at criticality which has already been noticed before several times [19,20,24]. Overall we can conclude, however, that our data is compatible with the exact 2D Ising value of ~ = 0.…”

“…The values for U* can be compared with previous MC estimates for the 2D Ising model on regular square lattices, U4"=0.615(10) [22] and U4* =0.611(1) [23], Poissonian random lattices, U4* =0.615(7) [24], fluctuating Regge triangulations, U4* =0.612(5) [19], or with an extremely precise transfer matrix computation yielding U4* =0.6106901(5) [25]. Since all our values for U4* in Table 1 are consistent with this most precise value, this gives further support that the critical behaviour of the asymmetric XY model is governed for all .12 ~ 0 by the 2D Ising universality class.…”

Monte Carlo studies of phase transitions and critical phenomena

“…£ ÐÂËÃÑÎÇÇ ÒÑÎÐÑÏ ÄËAEÇ ÕÇÑÓËâ ÍÑÐÇÚÐÑ-ÓÂÊÏÇÓÐÑÅÑ ÔÍÇÌÎËÐÅ (¬²³) ÒÓÇAEÔÕÂÄÎÇÐÂ Ä [96]. ªAEÇË, ÊÂÎÑÉÇÐÐÞÇ Ä àÕÑÌ ÕÇÑÓËË, ÒÑÊÄÑÎâáÕ àÍÔÕÓÂ-ÒÑÎËÓÑÄÂÕß ®¬ ÓÇÊÖÎßÕÂÕÞ, ÒÑÎÖÚÇÐÐÞÇ AEÎâ ÔËÔÕÇÏ Ô ÍÑÐÇÚÐÞÏË ÓÂÊÏÇÓÂÏË, Í ÕÇÓÏÑAEËÐÂÏËÚÇÔÍÑÏÖ ÒÓÇAEÇÎÖ (N L 3 3 I) Ë ÛËÓÑÍÑ ËÔÒÑÎßÊÖáÕÔâ [119,120,128,147,148]. ³ÑÅÎÂÔÐÑ àÕÑÌ ÕÇÑÓËË ÔÄÑÃÑAEÐÂâ àÐÇÓÅËâ AEÎâ AEÑÔÕÂÕÑÚÐÑ ÃÑÎßÛÑÌ ÔËÔÕÇÏÞ Ô ±¤µ ÒÓË ÕÇÏÒÇÓÂÕÖÓÇ T, ÃÎËÊÍÑÌ Í ÍÓËÕËÚÇÔÍÑÌ ÕÇÏÒÇÓÂÕÖÓÇ T c ÃÇÔÍÑÐÇÚÐÑÌ ÔËÔÕÇÏÞ, ÏÑÉÇÕ ÃÞÕß ÒÓÇAEÔÕÂÄÎÇÐÂ Ä ÄËAEÇ…”

Phase Transitions in Equilibrium and Non-Equilibrium Models on Some Topologies

“…Their results showed evidence that IM on UVD random lattices has the same critical behavior of the IM on SL. Posteriorly, Janke et al [28,51], using a global MC update algorithm [52], reweighting techniques [53] and finite size scaling analysis, studied the IM on UVD random lattices. Their results were similar to those found by Espriu et al [50], showing that the IM on UVD random lattices belongs to the universality same class of the IM on SL.…”