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Physical review. E

Universality class of the structural phase transition in the normal phase of cuprate superconductors

M. N. Najafi, Ali Tavana

Published Aug 8, 2016• 5 citations
Publisher

Abstract

The tetragonal-orthorhombic structural phase transition of oxygen atoms in the basal plane of YBa_{2}Cu_{3}O_{6+δ} high-T_{C} cuprate superconductors is studied numerically. By mapping the system onto the asymmetric next-nearest-neighbor Ising model, we characterize this phase transition. Results indicate the degrees of critical behavior. We show that this phase transition occurs at the temperature T_{C}≃0.148eV in the thermodynamic limit. By analyzing the critical exponents, it is found that this universality class displays some common features, with the two-dimensional three-state Potts model universality class, although the possibility of other universality classes cannot be ruled out. Conformal invariance at T=T_{c} is investigated using the Schramm-Loewner evolution (SLE) technique, and it is found that the SLE diffusivity parameter for this system is 3.34±0.01.

DOI
10.1103/physreve.94.022110

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The tetragonal-orthorhombic structural phase transition of oxygen atoms in the basal plane of YBa_{2}Cu_{3}O_{6+δ} high-T_{C} cuprate superconductors is studied numerically. By mapping the system onto the asymmetric next-nearest-neighbor Ising model, we characterize this phase transition. Results indicate the degrees of critical behavior. We show that this phase transition occurs at the temperature T_{C}≃0.148eV in the thermodynamic limit. By analyzing the critical exponents, it is found that this universality class displays some common features, with the two-dimensional three-state Potts model universality class, although the possibility of other universality classes cannot be ruled out. Conformal invariance at T=T_{c} is investigated using the Schramm-Loewner evolution (SLE) technique, and it is found that the SLE diffusivity parameter for this system is 3.34±0.01.
The class of high T c superconductors share one common structural aspect, the existence of planes of copper and oxygen ions.These planes are thought to be the source of the superconducting behaviour.They can be represented as a two-dimensional lattice of ions, which facilitates their study using numerical models.One such model is the t -J model.In most studies utilising numerical models, the planes have been considered isotropic.However, recent analysis of cuprate structure has illustrated that this may not be representative of the copper oxide planes.A number of cuprate structures exhibit different phases in which the planes are not isotropic, such as the low temperature orthorhombic and low temperature tetragonal phases.This work will examine the effects of introducing anisotropy into the t -J model in order to understand how these phases affect the results gained from numerical studies.
Phase transitions and critical characteristics of the layered antiferromagnetic Ising model in the case of a cubic lattice with next-nearest-neighbor intralayer interactions are studied in the framework of the Monte Carlo method implementing the replica algorithm. The characteristics of the phase transitions are analyzed within the histogram method and with the Binder cumulants. For the model under study, it is found that the transition from the superantiferromagnetic phase to the paramagnetic one is a second order phase transition. The static critical exponents for the specific heat α, susceptibility γ, order parameter β, correlation radius ν, and the Fisher exponent η are calculated using the finite-size scaling theory. It is shown that the three-dimensional Ising model for the cubic lattice with next-nearest-neighbor interactions belongs to the same universality class of critical behavior as the completely frustrated three-dimensional Ising model.
We study the surface criticality of a three-state antiferromagnetic Potts model on a simple cubic lattice, whose bulk critical behavior belongs to the universality class of the XY model because of emergent O(2) symmetry. We find that the surface antiferromagnetic next-nearest-neighboring interactions can drive the extraordinary-log phase to an ordinary phase, and the transition between the two phases belongs to the universality class of the well-known special transition of the XY model. Further enhancing the surface next-nearest-neighboring interactions, the extraordinary-log phase reappears, but the main critical behaviors are shown in the sublattices; the special point between the ordinary phase and the sublattice extraordinary-log phase belongs to a different universality class.
Abstract The Monte Carlo method has been used to study phase transitions and critical properties of the antiferromagnetic 3-state Potts model on a body-centered cubic lattice with interactions of the first (J1) and second (J2) nearest neighbors. The competition of exchange interactions in the range –2/3 < J2 < 0 was determined to result in a phase separation. In the low-temperature region, an ordered phase, lying inside the phase with broken sublattice symmetry, was found. The magnetic structures of the ground state corresponding to different regions of the phase diagram have been obtained. The analysis of the phase transition order has been carried out using the Binder cumulant method and the histogram method. It has been revealed that the interaction of the second nearest neighbors leads to a change in the type of phase transition. Static critical exponents have been calculated based on scaling relations. The critical exponents correspond to the universality class of the three-dimensional XY model.
A generic two-dimensional disordered topological superconductor in symmetry class D exhibits rich phenomenology and multiple phases: diffusive thermal metal (DTM), Anderson insulator (AI), and thermal quantum Hall (TQH) phase (a topological superconductor). We numerically investigate the phase diagram of a lattice model of such class-D superconductor, specifically focusing on transitions between the phases and the associated universal critical behaviors. We confirm the existence of a tricritical point and its repulsive nature at the point on the phase diagram where the three phases meet. We characterize the critical behaviors at various critical points and the tricritical point using numerical evaluation of the localization length, the conductance (or conductivity), and the density of states. We conclude that the two metal-insulator transitions (DTM-TQH and DTM-AI) belong to the same universality class, whereas the tricritical point represents a distinct universality class.
The anisotropic triangular nearest-neighbor Ising model, with antiferromagnetic interactions, is studied. The phase diagram, as a function of temperature and field, has a complex structure. Two commensurate ordered phases are found. The transition to one is Ising-type. The second is reached from the disordered phase in one of two ways: either via an intermediate uniaxial incommensurate phase---which is reached at high temperatures by a Kosterlitz-Thouless transition and at low temperatures undergoes an incommensurate-commensurate transition---or by a single continuous transition. The latter transition is in the same universality class as the chiral three-state Potts model, with thermal exponent within 4% of that of the three-state Potts model. These two transition regimes are found to be separated by a Lifshitz point. The phase diagram and critical behavior were determined by analytical (symmetry analysis and free-fermion approximation) as well as numerical (phenomenological renormalization-group and Monte Carlo) methods.