Related papers: Phase transitions in the $\mathbb{Z}_p$ and U(1) c…
The two-dimensional $q$-state clock model for $q \geq 5$ undergoes two Berezinskii-Kosterlitz-Thouless (BKT) phase transitions as temperature decreases. Here we report an extensive worm-type simulation of the square-lattice clock model for…
Classical 2D clock model is known to have a critical phase with Berezinskii-Kosterlitz-Thouless(BKT) transitions. These transitions have logarithmic corrections which make numerical analysis difficult. In order to resolve this difficulty,…
We explore possible synchronization in two-dimensional (2D) locally coupled discrete-state oscillators under thermal fluctuations, using the self-rotating $q$-state clock model as a prototype. Large-scale Monte Carlo simulations reveal that…
In a two-dimensional (2D) spin system, the XY model, characterized by planar rotational symmetry, exhibits a unique phenomenon known as the Berezinskii-Kosterlitz-Thouless (BKT) transition. In contrast, the clock model, which introduces…
The Berezinskii-Kosterlitz-Thouless (BKT) transitions of the six-state clock model on the square lattice are investigated by means of the corner-transfer matrix renormalization group method. The classical analogue of the entanglement…
We perform the state-of-the-art tensor network simulations directly in the thermodynamic limit to clarify the critical properties of the $q$-state clock model on the square lattice. We determine accurately the two phase transition…
The $q-$state clock model, sometimes called the discrete $XY$ model, is known to show a second-order (symmetry breaking) phase transition in two-dimension (2D) for $q\le 4$ ($q=2$ corresponds to the Ising model). On the other hand, the…
The Berezinskii-Kosterlitz-Thouless (BKT) transitions of the six-state clock model on the square lattice are investigated by means of the corner-transfer matrix renormalization group method. A classical analog of the entanglement entropy…
We demonstrate that a machine learning technique with a simple feedforward neural network can sensitively detect two successive phase transitions associated with the Berezinskii-Kosterlitz-Thouless (BKT) phase in q-state clock models…
We study the two-dimensional $q$-state clock model in the presence of an additional $p$-fold symmetry-breaking crystalline field using Monte Carlo simulations. While the pure clock model exhibits Berezinskii--Kosterlitz--Thouless (BKT)…
The Berezinsky-Kosterlitz-Thouless (BKT) type phase transitions in two-dimensional systems with internal abelian continuous symmetries are investigated. The necessary conditions for they can take place are: 1) conformal invariance of the…
The p-state clock model in two dimensions is a system of discrete rotors with a quasi-liquid phase in a region T1 < T < T2 for p > 4. We show that, for p > 4 and above a temperature Teu, all macroscopic thermal averages, such as energy or…
The Berezinskii-Kostelitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry-breaking, where a quasi-ordered phase, characterized by a power law scaling of the correlation functions at…
The Berezinskii-Kosterlitz-Thouless (BKT) transition is a typical topological phase transition defined between binding and unbinding states of vortices and antivortices, which is not accompanied by spontaneous symmetry breaking. It is known…
We study $q$-state clock models of regular and Villain types with $q=5,6$ using cluster-spin updates and observed double transitions in each model. We calculate the correlation ratio and size-dependent correlation length as quantities for…
We clarify the long-standing controversy concerning the behavior of the ground state fidelity in the vicinity of a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type in one-dimensional systems. Contrary to the prediction…
Motivated by the physics of coherently coupled, ultracold atom-molecule mixtures, we investigate a classical model possessing the same symmetry -- namely a $U(1)\times \mathbb{Z}_2$ symmetry, associated with the mass conservation in the…
We investigate the partition function zeros of the two-dimensional $p$-state clock model in the complex temperature plane by using the Wang-Landau method. For $p=5$, $6$, $8$, and $10$, we propose a modified energy representation to…
We consider two-dimensional $q$-state quantum clock models with quantum fluctuations connecting states with clock transitions with different choices for matrix elements. We study the quantum phase transitions in these models using quantum…
We study the fidelity approach to quantum phase transitions (QPTs) and apply it to general thermal phase transitions (PTs). We analyze two particular cases: the Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of…