Article
Critical Binder cumulant of twodimensional Ising models
Physics of Condensed Matter (Impact Factor: 1.28). 04/2006; 51(2):223228. DOI: 10.1140/epjb/e2006002097
Source: arXiv

Article: Location of the Pottscritical end point in the frustrated Ising model on the square lattice
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ABSTRACT: We report on Monte Carlo simulations for the twodimensional frustrated $J_1$$J_2$ Ising model on the square lattice. Recent analysis has shown that for the phase transition from the paramagnetic state to the antiferromagnetic collinear state different phasetransition scenarios apply depending on the value of the frustration $J_2 / J_1$. In particular a region with critical AshkinTellerlike behavior, i.e., a secondorder phase transition with varying critical exponents, and a noncritical region with firstorder indications were verified. However, the exact transition point $[J_2/J_1]_C$ between both scenarios was under debate. In this paper we present Monte Carlo data which strengthens the conclusion of Jin \et [Phys. Rev. Lett. \textbf{108}, 045702 (2012)] that the transition point is at a value of $J_2/J_1 \approx 0.67$ and that doublepeak structures in the energy histograms for larger values of $J_2/J_1$ are unstable in a scaling analysis.Physical Review B 10/2012; 86(13):134410. · 3.66 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider the thermal phase transition from a paramagnetic to stripeantiferromagnetic phase in the frustrated twodimensional squarelattice Ising model with competing interactions J1<0 (nearest neighbor, ferromagnetic) and J2 >0 (second neighbor, antiferromagnetic). The striped phase breaks a Z4 symmetry and is stabilized at low temperatures for g=J2/J1>1/2. Despite the simplicity of the model, it has proved difficult to precisely determine the order and the universality class of the phase transitions. This was done convincingly only recently by Jin et al. [PRL 108, 045702 (2012)]. Here, we further elucidate the nature of these transitions and their anomalies by employing a combination of cluster meanfield theory, Monte Carlo simulations, and transfermatrix calculations. The J1J2 model has a line of very weak firstorder phase transitions in the whole region 1/2<g<g*, where g* = 0.67(1). Thereafter, the transitions from g above g* are continuous and can be fully mapped, using universality arguments, to the critical line of the well known AshkinTeller model from its 4state Potts point to the decoupled Ising limit. We also comment on the pseudofirstorder behavior at the Potts point and its neighborhood in the AshkinTeller model on finite lattices, which in turn leads to the appearance of similar effects in the vicinity of the multicritical point g* in the J1J2 model. The continuous transitions near g* can therefore be mistaken to be firstorder transitions, and this realization was the key to understanding the paramagneticstriped transition for the full range of g>1/2. Most of our results are based on Monte Carlo calculations, while the cluster meanfield and transfermatrix results provide useful methodological benchmarks for weakly firstorder behaviors and AshkinTeller criticality.Physical review. B, Condensed matter 12/2012; 87(14). · 3.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the dependence of the critical Binder cumulant of the magnetization and the largest FortuinKasteleyn cluster on the boundary conditions and aspect ratio of the underlying square Ising lattices. By means of the SwendsenWang algorithm, we generate numerical data for large system sizes and we perform a detailed finitesize scaling analysis for several values of the aspect ratio r, for both periodic and free boundary conditions. We estimate the universal probability density functions of the largest FortuinKasteleyn cluster and we compare it to those of the magnetization at criticality. It is shown that these probability density functions follow similar scaling laws, and it is found that the values of the critical Binder cumulant of the largest FortuinKasteleyn cluster are upper bounds to the values of the respective orderparameter's cumulant, with a splitting behavior for large values of the aspect ratio. We also investigate the dependence of the amplitudes of the magnetization and the largest FortuinKasteleyn cluster on the aspect ratio and boundary conditions. We find that the associated exponents, describing the aspectratio dependencies, are different for the magnetization and the largest FortuinKasteleyn cluster, but in each case are independent of boundary conditions.Physical Review E 04/2014; 89(41):042103. · 2.31 Impact Factor
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