Critical behavior of the two-dimensional<i>XY</i>model

Gupta, Rajan; Baillie, C.F.

doi:10.1103/physrevb.45.2883

Cited by 201 publications

(244 citation statements)

References 14 publications

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“…This intersection exists only if x is less than the critical value x c < π/8, to be estimated below. Fortunately, we do not need to find this intersection explicitly since we already know the critical value of the effective coupling K eff , which is the usual critical coupling of the classical XY model, K (c) eff = K XY c ≈ 1.1186 [37]. Therefore, the values of the two critical couplings are…”

Section: B Renormalization Group Analysismentioning

confidence: 99%

“…The critical temperature is obtained from the intersection of the separatrix with the initial conditions given in Eqs. (36) and (37). This intersection exists only if x is less than the critical value x c < π/8, to be estimated below.…”

Section: B Renormalization Group Analysismentioning

confidence: 99%

“…At low temperatures the energy to create an isolated vortex grows logarithmically with the size of the system, therefore excitations are created as bounded vortex-antivortex pairs. As the temperature increases, the vortex pair density increases until they unbind at a critical dimensionless temperature T BKT = 0.894(5) [37,40]. The BKT scenario is best understood in terms of a renormalization group (RG) analysis [34,35].…”

Section: B Renormalization Group Analysismentioning

confidence: 99%

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Critical properties of two-dimensional Josephson-junction arrays with zero-point quantum fluctuations

Rojas

José

1996

Phys. Rev. B

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We present results from an extensive analytic and numerical study of a twodimensional model of a square array of ultrasmall Josephson junctions. We include the ultrasmall self and mutual capacitances of the junctions, for the same parameter ranges as those produced in the experiments. The model Hamiltonian studied includes the Josephson, E J , as well as the charging, E C , energies between superconducting islands. The corresponding quantum partition function is expressed in different calculationally convenient ways within its path-integral representation. The phase diagram is analytically studied using a WKB renormalization group (WKB-RG) plus a self-consistent harmonic approximation (SCHA) analysis, together with non-perturbative quantum Monte Carlo simulations. Most of the results presented here pertain to the superconductor to normal (S-N) region, although some results for the insulating to normal (I-N) region are also included. We find very good agreement between the WKB-RG and QMC results when compared to the experimental data. To fit the data, we only used the experimentally determined capacitances as fitting parameters. The WKB-RG analysis in the S-N region predicts a low temperature instability i.e. a Quantum Induced Transition (QUIT). We carefully analyze the possible existence of the QUIT via the QMC simulations and carry out a finite size analysis of T QU IT as a function of the magnitude of imaginary time axis L τ . We find that for some relatively large values of α = E C E J (1 ≤ α ≤ 2.25), the L τ → ∞ limit does appear to give a non-zero T QU IT , while for α ≥ 2.5, T QU IT = 0. We use the SCHA to analytically understand the L τ dependence of the QMC results with good agreement between them. Finally, we also carried out a WKB-RG analysis in the I-N region and found no evidence of a low temperature QUIT, up to lowest order in α −1 .

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Section: B Renormalization Group Analysismentioning

confidence: 99%

Section: B Renormalization Group Analysismentioning

confidence: 99%

Section: B Renormalization Group Analysismentioning

confidence: 99%

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Critical properties of two-dimensional Josephson-junction arrays with zero-point quantum fluctuations

Rojas

José

1996

Phys. Rev. B

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“…In [16], all simulations were at the KT temperature T = 0.90 [23]. In earlier work, Luo et al [24] have additionally studied some lower temperature within the KT phase.…”

Section: Comparison With Simulation Datamentioning

confidence: 99%

Random walks in logarithmic and power-law potentials, nonuniversal persistence, and vortex dynamics in the two-dimensionalXYmodel

2000

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The Langevin equation for a particle ('random walker') moving in d-dimensional space under an attractive central force and driven by a Gaussian white noise is considered for the case of a power-law force, F (r) ∼ −r −σ . The 'persistence probability', P0(t), that the particle has not visited the origin up to time t, is calculated for a number of cases. For σ > 1, the force is asymptotically irrelevant (with respect to the noise), and the asymptotics of P0(t) are those of a free random walker. For σ < 1, the noise is (dangerously) irrelevant and the asymptotics of P0(t) can be extracted from a weak noise limit within a path-integral formalism employing the Onsager-Machlup functional.The case σ = 1, corresponding to a logarithmic potential, is most interesting because the noise is exactly marginal. In this case, P0(t) decays as a power-law, P0(t) ∼ t −θ with an exponent θ that depends continuously on the ratio of the strength of the potential to the strength of the noise. This case, with d = 2, is relevant to the annihilation dynamics of a vortex-antivortex pair in the two-dimensional XY model. Although the noise is multiplicative in the latter case, the relevant Langevin equation can be transformed to the standard form discussed in the first part of the paper. The mean annihilation time for a pair initially separated by r is given by t(r) ∼ r 2 ln(r/a) where a is a microscopic cut-off (the vortex core size). Implications for the nonequilibrium critical dynamics of the system are discussed and compared to numerical simulation results.

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“…The two critical lines representing the nonequilibrium disorder-long range order transitions meet at a temperature 1/β c ≈ 0.89. This is the same as the KT critical temperature [27], leading us to conclude that the ordered regions of the diagram meet at a line corresponding to the low temperature equilibrium KT phase.…”

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confidence: 73%

Phase diagram for a two-dimensional, two-temperature, diffusiveXYmodel

2010

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Using Monte Carlo simulations, we determine the phase diagram of a diffusive two-temperature conserved order parameter XY model. When the two temperatures are equal the system becomes the equilibrium XY model with the continuous Kosterlitz-Thouless (KT) vortex-antivortex unbinding phase transition. When the two temperatures are unequal the system is driven by an energy flow from the higher temperature heat-bath to the lower temperature one and reaches a far-fromequilibrium steady state. We show that the nonequilibrium phase diagram contains three phases: A homogenous disordered phase and two phases with long range, spin texture order. Two critical lines, representing continuous phase transitions from a homogenous disordered phase to two phases of long range order, meet at the equilibrium KT point. The shape of the nonequilibrium critical lines as they approach the KT point is described by a crossover exponent ϕ = 2.52 ± 0.05. Finally, we suggest that the transition between the two phases with long-range order is first-order, making the KT-point where all three phases meet a bicritical point. Much of the research in the statistical physics of nonequilibrium sytems has been directed toward understanding how universal equilibrium critical phenomena are affected by dynamical nonequilibrium perturbations. Field-theoretical studies have indicated that the effects of nonequilibrium dynamics are drastic in systems where detailed balance violation is coupled with conserved anisotropic dynamics [1]. In these systems, effective long range interactions can be induced by the local dynamics producing a critical behavior that is remarkably different from the one of the corresponding unperturbed, equilibrium, systems [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].In this paper, we present the phase diagram for a two-dimensional two-temperature diffusive conserved order parameter XY model. The system evolves through Kawasaki spin-exchange dynamics [19]. Thus, the dynamics is purely relaxational with no reversible mode couplings, and corresponds to Model B of Ref. 20. Long range order can exist in nonequilibrium steady states of this system due to the effective long range interactions generated by the anisotropic diffusive dynamics that occurs in that regime. The ordered phase is characterized by the appearance of standing spin waves, or spin textures, oriented along the direction of lower temperature. The system exhibits a nonequilibrium disorderlong-range order transition that is in the same universality class as an equilibrium model with dipole interactions [11,14]. Note that our model reduces to the equilibrium XY model in the limit where both temperatures are equal. Also, the Mermin-Wagner theorem states that there is no spontaneous symmetry breaking in equilibrium systems with continuous symmetry of * Present address: Max Planck Institut für Physik complexer Systeme, Nöthnitzerstraße 38, 01187 Dresden, Germany.the order parameter and dimension d = 2 [21]. Thus, no long-range ordered phase is observed in the tw...

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Critical behavior of the two-dimensionalXYmodel

Cited by 201 publications

References 14 publications

Critical properties of two-dimensional Josephson-junction arrays with zero-point quantum fluctuations

Critical properties of two-dimensional Josephson-junction arrays with zero-point quantum fluctuations

Random walks in logarithmic and power-law potentials, nonuniversal persistence, and vortex dynamics in the two-dimensionalXYmodel

Phase diagram for a two-dimensional, two-temperature, diffusiveXYmodel

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