A MEAN FIELD STUDY OF THE PHASE TRANSITIONS IN A CLASS OF SYSTEMS WITH COMPLEX ORDER PARAMETERS

1994 ◽  
Vol 08 (28) ◽  
pp. 3963-3986
Author(s):  
EVGENIA J. BLAGOEVA
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Order Parameter ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Unconventional Superconductors ◽  
Complex Order ◽  
The Mean ◽  
Expansion Coefficients

A generalized Landau free energy for a complex order parameter expanded up to sixth-order is investigated using group theoretical arguments and the mean-field approximation. Results for the phase transitions that occur are presented. The phase diagram for all allowed values of the expansion coefficients is constructed with an emphasis placed on the influence of the anisotropy in the order parameter space. The results can be used in discussions of unconventional superconductors and modulated structural and magnetic orderings.

Partially Disordered State in the Frustrated Heisenberg Ferrimagnet

2014 ◽  
Vol 215 ◽  
pp. 55-60 ◽  
Author(s):  
Sergey N. Martynov
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Magnetic Phase ◽  
Mean Field ◽  
Exchange Interactions ◽  
Field Approximation ◽  
Magnetic Phase Transitions ◽  
Mean Field Approximation ◽  
The Mean ◽  
Competition Parameter

A model for the description of two-subsystem Heisenberg ferrimagnet with frustrated intersubsystem exchange and competition between exchange interactions in a subsystem is proposed. The conditions of the existence of noncollinear Yafet-Kittel state and partially ordered magnetic structure are investigated. The phase diagram of competition parameter vs temperature is obtained in the mean field approximation. The peculiarities of the succesive magnetic phase transitions are considered.

scholarly journals Inhomogeneous chiral condensates in low-energy color-superconductivity models of QCD

2021 ◽  
Author(s):  
◽  
Philip Lakaschus
Keyword(s):  
Phase Diagram ◽  
Mean Field ◽  
Field Approximation ◽  
Chiral Condensate ◽  
Dispersion Relations ◽  
Mean Field Approximation ◽  
Color Superconductivity ◽  
Diquark Model ◽  
Coexistence Phase ◽  
The Mean

This thesis explores the phase diagrams of the Nambu--Jona-Lasinio (NJL) and quark-meson (QM) model in the mean-field approximation and beyond. The focus lies in the investigation of the interplay between inhomogeneous chiral condensates and two-flavor color superconductivity. In the first part of this thesis, we study the NJL model with 2SC diquarks in the mean-field approximation and determine the dispersion relations for quasiparticle excitations for generic spatial modulations of the chiral condensate in the presence of a homogeneous 2SC-diquark condensate, provided that the dispersion relations in the absence of color superconductivity are known. We then compare two different Ansätze for the chiral order parameter, the chiral density wave (CDW) and the real-kink crystal (RKC). For both Ansätze we find for specific diquark couplings a so-called coexistence phase where both the inhomogeneous chiral condensate and the diquark condensate coexist. Increasing the diquark coupling disfavors the coexistence phase in favor of a pure diquark phase. On the other hand, decreasing the diquark coupling favors the inhomogeneous phase over the coexistence phase. In the second part of this thesis the functional renormalization group is employed to study the phase diagram of the quark-meson-diquark model. We observe that the region of the phase diagram found in previous studies, where the entropy density takes on unphysical negative values, vanishes when including diquark degrees of freedom. Furthermore, we perform a stability analysis of the homogeneous phase and compare the results with those of previous studies. We find that an increasing diquark coupling leads to a smaller region of instability as the 2SC phase extends to a smaller chemical potential. We also find a region where simultaneously an instability occurs and a non-vanishing diquark condensate forms, which is an indication of the existence of a coexistence phase in accordance with the results of the first part of this work.

Phase Transitions and the Ising Model

2019 ◽  
pp. 423-446
Author(s):  
Robert H. Swendsen
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Landau Theory ◽  
Magnetic Moments ◽  
Mean Field ◽  
Higher Dimensions ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ising Chain ◽  
The Mean

Chapter 17 presented one example of a phase transition, the van der Waals gas. This chapter provides another, the Ising model, a widely studied model of phase transitions. We first give the solution for the Ising chain (one-dimensional model), including the introduction of the transfer matrix method. Higher dimensions are treated in the Mean Field Approximation (MFA), which is also extended to Landau theory. The Ising model is deceptively simple. It can be defined in a few words, but it displays astonishingly rich behavior. It originated as a model of ferromagnetism in which the magnetic moments were localized on lattice sites and had only two allowed values.

ANALYTICAL EXPRESSIONS OF THE ORDER PARAMETERS NEAR THE TRANSITION TEMPERATURES IN THE SPIN-3/2 ISING SYSTEM WITH BILINEAR AND BIQUADRATIC INTERACTIONS

2006 ◽  
Vol 20 (04) ◽  
pp. 455-467 ◽  
Author(s):  
OSMAN CANKO ◽  
MUSTAFA KESKIN
Keyword(s):  
Phase Transitions ◽  
Mean Field ◽  
Field Approximation ◽  
Irreversible Thermodynamics ◽  
Order Parameters ◽  
Mean Field Approximation ◽  
Transition Temperatures ◽  
Ising System ◽  
The Mean ◽  
Analytical Expressions

Analytical expressions of the order parameters near the transition temperatures in the spin-3/2 Ising system with bilinear (J) and biquadratic (K) interactions are presented for various values of J/K. First, we obtain the free energy expression and the equations to determine order parameters by using the mean-field approximation. Then, the order parameters are expressed in the vicinity of the transition temperatures in which these expressions are very important to study the dynamics of the system by means of Onsager's theory of irreversible thermodynamics. Hence, we investigate the phase transitions occurring in the system and also obtain two tricritical points analytically. Finally, the specific heat and magnetic susceptibility are calculated and an argument about the critical exponents at the second-order phase transitions and tricritical points is given.

Modulated Phases on the FCC(110) Surfaces with Adsorbate-Induced Reconstructions

2003 ◽  
Vol 10 (02n03) ◽  
pp. 189-194
Author(s):  
Min Kang ◽  
Makoto Kaburagi
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Correlation Function ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Modulated Phases ◽  
The Mean ◽  
Beg Model

We theoretically investigate the fcc(110) surfaces with missing row reconstructions induced by adatoms using the Blume–Emmery–Griffith (BEG) model. In the model, Kij is introduced to denote interactions between surface atoms and Jij to describe interactions between dipoles. The investigation by the mean field approximation has predicted that there appear modulated phases on the surfaces as the next-nearest-neighbor (NNN) and the nearest-neighbor (NN) interactions along the [001] direction become competitive. In this study, Monte Carlo simulations are performed to confirm the prediction. A correlation function defined by concentration operators in wave vector q space is calculated. The results show that the concentration modulations appear. The temperature versus the ratio of the NNN interaction K2 to the NN interaction K1 phase diagram is obtained. The possible features of the modulated phases in experiments are discussed.

scholarly journals Short-ranged interaction effects on Z2 topological phase transitions: The perturbative mean-field method

2015 ◽  
Vol 29 (06) ◽  
pp. 1530005 ◽  
Author(s):  
Hsin-Hua Lai ◽  
Hsiang-Hsuan Hung
Keyword(s):  
Phase Transitions ◽  
Analytical Approach ◽  
Mean Field ◽  
Field Approximation ◽  
Quantum Spin ◽  
Mean Field Approximation ◽  
Topological Phase ◽  
Self Consistent ◽  
The Mean ◽  
Topological Phase Transitions

Time-reversal symmetric topological insulator (TI) is a novel state of matter that a bulk-insulating state carries dissipationless spin transport along the surfaces, embedded by the Z2 topological invariant. In the noninteracting limit, this exotic state has been intensively studied and explored with realistic systems, such as HgTe/(Hg, Cd)Te quantum wells. On the other hand, electronic correlation plays a significant role in many solid-state systems, which further influences topological properties and triggers topological phase transitions. Yet an interacting TI is still an elusive subject and most related analyses rely on the mean-field approximation and numerical simulations. Among the approaches, the mean-field approximation fails to predict the topological phase transition, in particular at intermediate interaction strength without spontaneously breaking symmetry. In this paper, we develop an analytical approach based on a combined perturbative and self-consistent mean-field treatment of interactions that is capable of capturing topological phase transitions beyond either method when used independently. As an illustration of the method, we study the effects of short-ranged interactions on the Z2 TI phase, also known as the quantum spin Hall (QSH) phase, in three generalized versions of the Kane–Mele (KM) model at half-filling on the honeycomb lattice. The results are in excellent agreement with quantum Monte Carlo (QMC) calculations on the same model and cannot be reproduced by either a perturbative treatment or a self-consistent mean-field treatment of the interactions. Our analytical approach helps to clarify how the symmetries of the one-body terms of the Hamiltonian determine whether interactions tend to stabilize or destabilize a topological phase. Moreover, our method should be applicable to a wide class of models where topological transitions due to interactions are in principle possible, but are not correctly predicted by either perturbative or self-consistent treatments.

scholarly journals Phase Diagram of the Attractive Kane-Mele-Hubbard Model at Half Filling

Atoms ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 58
Author(s):  
Zlatko Koinov
Keyword(s):  
Phase Diagram ◽  
Optical Lattices ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Recent Developments ◽  
Topological States ◽  
Half Filling ◽  
The Mean

Motivated by recent developments in the experimental study of ultracold atoms in graphene-like honeycomb optical lattices, we investigate superconductivity of the attractive Kane-Mele-Habbard (KMH) model with the next-nearest-neighbor (NNN) hoping at half filling. The mean-field approximation is used to study the phase diagram which interpolates the trivial and the non-trivial topological states. It is shown that: (a) when the NNN hoping is taken into account, one has to introduce two mean-field gap equations for the two sublattices, instead of a single gap when the NNN hopping is neglected, and (b) in the non-trivial topological region the phase diagram with the NNN hopping is significantly different compared to the phase diagram calculated previously, but without the NNN term. We also discuss the superconducting instability of the attractive KMH model that is driven by condensation of Cooperons.

ANTIFERROMAGNETISM AND HOLE CONCENTRATION IN THE LINEAR SPIN WAVE APPROXIMATION OF THE t-J MODEL

1994 ◽  
Vol 08 (02) ◽  
pp. 131-136 ◽  
Author(s):  
A. BELKASRI ◽  
J.L. RICHARD
Keyword(s):  
Spin Wave ◽  
Order Parameter ◽  
Degrees Of Freedom ◽  
Hole Concentration ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Antiferromagnetic State ◽  
Wave Approximation ◽  
The Mean

The interplay between antiferromagnetic state and low doping regime is studied within the framework of the t-J model. The staggered magnetization is calculated in the mean field approximation by separating spin and charge degrees of freedom. We have obtained that this order parameter decreases with increasing doping and vanishes for some critical hole concentration.

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