Ordered phase and scaling in $Z_n$ models and the three-state antiferromagnetic Potts model in three dimensions

We compute the effective potential $V_{\rm eff}(\phi)$ for one-component real scalar field $\phi$ in three Euclidean dimensions (3D) in the case of spontaneously broken symmetry, from the Monte Carlo simulation of the 3D Ising model in external field at temperatures approaching the phase transition from below. We study probability distributions of the order parameter on the lattices from $30^3$ to $74^3$, at $L/\xi \approx 10$. We find that, in close analogy with the symmetri...

The three-state Potts model is numerically investigated on three-dimensional simple cubic lattices of up to \(128^3\) volume, concentrating on the neighborhood of the first-order phase transition separating the ordered and disordered phases. The ordered phase is found to allow admixture of disordered domains induced by a long-range attraction acting between the two different non-favored spins. This phenomenon gives an explanation of why the first-order phase transitions assoc...

The QCD phase diagram at finite temperature and density is a topic of considerable interest. Although much progress has been made in recent years, some open questions remain. Even at zero density, the order of the transition for two light flavors of fermions has not yet been conclusively established. While considerable evidence exists in favor of a second-order transition for massless quarks and a crossover for massive quarks, some recent results with two flavors of staggered...

In the present article we analyze Non-Perturbative Renormalization Group flow equations in the order phase of $\mathbb{Z}_2$ and $O(N)$ invariant scalar models in the derivative expansion approximation scheme. We first address the behavior of the leading order approximation (LPA), discussing for which regulators the flow is smooth and gives a convex free energy and when it becomes singular. We improve the exact known solutions in the "internal" region of the potential and exp...

Topologically ordered quantum systems have robust physical properties, such as quasiparticle statistics and ground-state degeneracy, which do not depend on the microscopic details of the Hamiltonian. We consider topological phase transitions under a deformation such as an effective string tension on a $\mathbb{Z}_3$ topological state. This is studied in terms of the gauge-symmetry preserved quantum state renormalization group, first proposed by He, Moradi and Wen [Phys. Rev. ...

With the help of the replica exchange Monte Carlo method and the improved Monte Carlo renormalization-group scheme, we investigate over a wide area in the phase diagram of the Gaussian random field Ising model on the simple cubic lattice. We found that the phase transition at a weak random field belongs to the same universality class as the zero-temperature phase transition. We also present a possible scenario for the replica symmetry breaking transition.

The finite lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the $3$-state Potts model on the simple cubic lattice to order $z^{43}$ and the high-temperature expansion of the partition function to order $v^{21}$. We use the numerical data to show that the transition is first-order, and estimate the latent heat, the discontinuity in the magnetisation, and a number of other critica...

The unusual reentrant phenomenon is observed in the anisotropic 3-state Potts model on a gen- eralized Kagome lattice. By employing the linearized tensor renormalization group method, we find that the reentrance can appear in the region not only under a partial ordered phase as commonly known but also a phase without a local order parameter, which is uncovered to fall into the uni- versality of the Kosterlitz-Thouless (KT) type. The region of the reentrance depends strongly o...

We study the low-energy effective action $S_{eff}[\varphi]$ for the one-component real scalar field theory in three Euclidean dimensions in the symmetric phase, concentrating on its static part --- effective potential $V_{eff}(\varphi)$. It characterizes the approach to the phase transition in all systems that belong to the 3d Ising universality class. We compute it from the probability distributions of the average magnetization in the 3d Ising model in a homogeneous external...

We present the results of a Monte Carlo simulation of the antiferromagnetic RP(2) model in three dimensions. With finite-size scaling techniques we accurately measure the critical exponents and compare them with those of O(N) models. We are able to parameterize the corrections-to-scaling. The symmetry properties of the broken phase are also studied.