Related papers: Quantum Potts Models on the Sierpi\'nski Pyramid
The Potts model describes interacting spins with $Q$ different components, which is a direct generalization of the Ising model ($Q=2$). Compared to the existing exact solutions in 2D, the phase transitions and critical phenomena in the 3D…
The two-dimensional ferromagnetic anisotropic Ashkin-Teller model is investigated through a real-space renormalization-group approach. The critical frontier, separating five distinct phases, recover all the known exacts results for the…
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…
Since its introduction, the Potts model has gained widespread popularity across various fields due to its diverse applications. Even minor advancements in this model continue to captivate scientists worldwide, and small modifications often…
We consider the superstable cycles of the Q-state Potts (QSP) and the three-site interaction antiferromagnetic Ising (TSAI) models on recursive lattices. The rational mappings describing the models' statistical properties are obtained via…
Using Monte Carlo simulations and finite-size scaling, we study three-state Potts antiferromagnet on layered square lattice with two and four layers $L_z=2$ and $4$. As temperature decreases, the system develops quasi-long-range order via a…
Ground-state and thermodynamic properties of the one-dimensional Heisenberg antiferromagnet in which two S=1/2 and two S=1 spins are arranged alternatively are studied by a quantum Monte Carlo method and by analytical estimates. It is found…
The two-dimensional $q$-state clock models exhibit the Berezinskii-Kosterlitz-Thouless (BKT) transition for $q\geq5$ since they are a subset of the isotropic XY model. We examine the $6$-state clock model with an anisotropic deformation.…
Spin systems exposed to the influence of random magnetic fields are paradigmatic examples for studying the effect of quenched disorder on condensed-matter systems. In this context, previous studies have almost exclusively focused on systems…
We investigate the critical behavior and the duality property of the ferromagnetic $q$-state clock model on the square lattice based on the tensor-network formalism. From the entanglement spectra of local tensors defined in the original and…
I use the two-step density-matrix renormalization group method to extract the critical exponents $\beta$ and $\nu$ in the transition from a N\'eel $Q=(\pi,\pi)$ phase to a magnetically disordered phase with a spin gap. I find that the…
For the spin models with continuous symmetry on regular lattices and finite range of interactions the lower critical dimension is d=2. In two dimensions the classical XY-model displays Berezinskii-Kosterlitz-Thouless transition associated…
An overview of results of models of coupled quantum rotors is presented. We focus on rotors with dipolar and quadrupolar potentials in two and three dimensions, potentials which correspond to approximate descriptions of real molecules…
We present a renormalization group theory for the onset of Ising-nematic order in a Fermi liquid in two spatial dimensions. This is a quantum phase transition, driven by electron interactions, which spontaneously reduces the point-group…
We describe the quantum phase transitions in the ferromagnetic Dicke-Ising model using a Landau theory approach. The theory quantitatively captures the change from a second- to a first-order transition between the normal and superradiant…
The systems exhibiting quantum phase transitions (QPT) are investigated within the Ising model in the transverse field and Heisenberg model with easy-plane single-site anisotropy. Near QPT a correspondence between parameters of these models…
We establish an intriguing connection between quantum phase transitions and bifurcations in the reduced fidelity between two different reduced density matrices for quantum lattice many-body systems with symmetry-breaking orders. Our finding…
We investigate the critical behavior of the two-dimensional 8-state Potts model with an aperiodic distribution of the exchange interactions between nearest-neighbor rows. The model is studied numerically through intensive Monte Carlo…
We study the q-state Potts model on the simple cubic lattice with ferromagnetic interactions in one lattice direction, and antiferromagnetic interactions in the two other directions. As the temperature T decreases, the system undergoes a…
Within the canonical ensemble framework, this paper investigates the presence of higher-order transition signals in the $q$-state Potts model (for $q \geq 3$), using two geometric order parameters: isolated spins number and the average…