Wide crossover in the 3D Ashkin–Teller model

Computation of latent heat in the system of multi-component order parameter: 3D Ashkin-Teller model

“…The values obtained by scaling the positions of cumulants V α,L minima and of cumulants U α,L maxima shown in Fig. 6 gave us more accurate average critical value K 2 = 0.145189 (12). All obtained K 2 critical values are consistent within the error bars.…”

“…[6][7][8] and the papers cited therein). Moreover, the AT model shows the complex phase diagram and the Monte Carlo (MC) simulation results published so far suggest the possibility of the occurrence of the non-universal behavior also in the 3D AT model [9][10][11][12] which has been observed in the 2D one [13][14][15][16].…”

“…In Eqs 3and 4E n α L is the n-th moment of the interaction energy of α-degrees of freedom (α = s, σ or their product sσ) in Hamiltonian (1) separately, which is averaged over an ensemble of independent samples of the size L×L×L. The Challa and Lee-Kosterlitz cumulants have been adapted [4,10] by taking not only the whole Hamiltonian (1) for energy E as originally proposed by Challa et al [2] and by Lee and Kosterlitz [3], but also the Hamiltonian individual terms to be able to compute the latent heat for each component of the order parameter separately [10,12,19]. Of course, we make sure that the latent heat l H computed on the basis of the whole Hamiltonian (1) is equal to the sum of the latent heats l α (α = s, σ or their product sσ) coming from α degrees of freedom within their error bars.…”

“…A phase transition is qualified as continuous when V α,L = 2/3 and U α,L = 1 in their thermodynamic limits within the respective error bars [2,3,10,12,19]. For the error bar values of the extremes of these cumulants, we assume the maximum deviation of the points determined in our MC experiments from the fitted curves [10], as the uncertainties should always be rounded up.…”

“…Furthermore, the presence of characteristic minima of the Binder cumulant dependences on the K 2 coupling constant indicates the possibility of occurrence of latent heat for a phase transition [1,18] at a given coupling constant K 4 . Simultaneously, we independently use Challa and Lee-Kosterlitz cumulants, which require adaptation [10,12] to enable locating the phase transition point for the individual order parameter components and their contribution to the latent heat. Knowing the phase transition point position accurately enough, for strong phase transitions we can determine the latent heat value with a higher precision using the internal energy distribution histogram method [3] adapted to the considered system [4].…”