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Register a new userNematic order in a simple-cubic lattice-spin model with full-ranged dipolar interactions
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In a previous paper [Phys. Rev. E 90, 022506 (2014)], we had studied thermodynamic and structural properties of a three-dimensional simple-cubic lattice model with dipolar-like interaction, truncated at nearest-neighbor separation, for which the existence of an ordering transition at finite temperature had been proven mathematically; here we extend our investigation addressing the full-ranged counterpart of the model, for which the critical behavior had been investigated theoretically and experimentally. In addition the existence of an ordering transition at finite temperature had been proven mathematically as well. Both models exhibited the same continuously degenerate ground-state configuration, possessing full orientational order with respect to a suitably defined staggered magnetization (polarization), but no nematic second-rank order; in both cases, thermal fluctuations remove the degeneracy, so that nematic order does set in at low but finite temperature via a mechanism of order by disorder. On the other hand, there were recognizable quantitative differences between the two models as for ground-state energy and critical exponent estimates; the latter were found to agree with early Renormalization Group calculations and with experimental results.
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At low temperatures, some lattice spin models with simple ferromagnetic or antiferromagnetic interactions (for example nearest-neighbour interaction being isotropic in spin space on a bipartite three-dimensional lattice) produce orientationally ordered phases exhibiting nematic (second--rank) order, in addition to the primary first-rank one; on the other hand, in the Literature, they have been rather seldom investigated in this respect. Here we study the thermodynamic properties of a three-dimensional model with dipolar-like interaction. Its ground state is found to exhibit full orientational order with respect to a suitably defined staggered magnetization (polarization), but no nematic second-rank order. Extensive Monte Carlo simulations, in conjunction with Finite-Size Scaling analysis have been used for characterizing its critical behaviour; on the other hand, it has been found that nematic order does indeed set in at low temperatures, via a mechanism of order by disorder.
The edge-cubic spin model on square lattice is studied via Monte Carlo simulation with cluster algorithm. By cooling the system, we found two successive symmetry breakings, i.e., the breakdown of $O_h$ into the group of $C_{3h}$ which then freezes into ground state configuration. To characterize the existing phase transitions, we consider the magnetization and the population number as order parameters. We observe that the magnetization is good at probing the high temperature transition but fails in the analysis of the low temperature transition. In contrast the population number performs well in probing the low- and the high-$T$ transitions. We plot the temperature dependence of the moment and correlation ratios of the order parameters and obtain the high- and low-$T$ transitions at $T_h = 0.602(1)$ and $T_l=0.5422(2)$ respectively, with the corresponding exponents of correlation length $ u_h=1.50(1)$ and $ u_l=0.833(1)$. By using correlation ratio and size dependence of correlation function we estimate the decay exponent for the high-$T$ transition as $eta_h=0.260(1)$. For the low-$T$ transition, $eta_l = 0.267(1)$ is extracted from the finite size scaling of susceptibility. The universality class of the low-$T$ critical point is the same as the 3-state Potts model.
The classical Heisenberg antiferromagnet with uniaxial exchange anisotropy, the XXZ model, in a magnetic field on a simple cubic lattice is studied with the help of extensive Monte Carlo simulations. Analyzing, especially, various staggered susceptibilities and Binder cumulants, we present clear evidence for the meeting point of the antiferromagnetic, spin--flop, and paramagnetic phases being a bicritical point with Heisenberg symmetry. Results are compared to previous predictions based on various theoretical approaches.
We study the dynamical behavior of a square lattice Ising model with exchange and dipolar interactions by means of Monte Carlo simulations. After a sudden quench to low temperatures we find that the system may undergo a coarsening process where stripe phases with different orientations compete or alternatively it can relax initially to a metastable nematic phase and then decay to the equilibrium stripe phase through nucleation. We measure the distribution of equilibration times for both processes and compute their relative probability of occurrence as a function of temperature and system size. This peculiar relaxation mechanism is due to the strong metastability of the nematic phase, which goes deep in the low temperature stripe phase. We also measure quasi-equilibrium autocorrelations in a wide range of temperatures. They show a distinct decay to a plateau that we identify as due to a finite fraction of frozen spins in the nematic phase. We find indications that the plateau is a finite size effect. Relaxation times as a function of temperature in the metastable region show super-Arrhenius behavior, suggesting a possible glassy behavior of the system at low temperatures.
This paper has been withdrawn by the authors due to a possible inconsistency in the program code.
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