Phase transitions in the uniformly frustrated<i>XY</i>model with frustration parameter<i>f</i>=1/3 studied with use of the microcanonical Monte Carlo technique

Lee, Sooyeul; Lee, Koo-Chul

doi:10.1103/physrevb.52.6706

Cited by 9 publications

(16 citation statements)

References 14 publications

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“…This can give the impression of separate transitions for small system sizes. This impression is enhanced by the presence of a shoulder in the specific heat at intermediate system sizes [9]. For the larger system sizes, we see this shoulder merge with the main peak and for L = 84 and L = 96 it is no longer discernible.…”

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confidence: 75%

“…Clearly, Y is strongly renormalized from its bare value and attempting to fit scaling relations for the f = 0 case [9] without taking this into account seems questionable. We see two possible interpretations of our result.…”

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confidence: 99%

“…Lee and Lee [9] claim to find separate, closely spaced transitions, for the breaking of Z 2 and Z 3 . One explanation for their conflicting results comes from the small system sizes (L ≤ 42) used in their analysis.…”

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confidence: 99%

“…Since this effect is the same for all states, it cancels when calculating M . Using the real and imaginary parts of ρ k± in addition to j m ±1,j , calculated from the direct vortex lattice as in [9], we can find the five independent m σ,j .…”

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confidence: 99%

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Domain Walls and Phase Transitions in the Frustrated Two-DimensionalXYModel

Denniston

Tang²

1997

Phys. Rev. Lett.

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We compare the critical properties of the two-dimensional (2D) XY model in a transverse magnetic field with filling factors f = 1/3 and 2/5. To obtain a comparison with recent experiments, we investigate the effect of weak quenched bond disorder for f = 2/5. A finite-size scaling analysis of extensive Monte Carlo simulations strongly suggests that the critical exponents of the phase transition for f = 1/3 and for f = 2/5 with disorder, fall into the 2D Ising model universality class. Studying the possible domain walls in the system provides some explanations for our results. 64.70.Rh, 05.70.Fh, 64.60.Fr, 74.50.+r The frustrated XY model provides a convenient framework to study a variety of fascinating phenomena displayed by numerous physical systems. One experimental realization of this model is in two-dimensional arrays of Josephson junctions and superconducting wire networks [1][2][3]. A perpendicular magnetic field induces a finite density of circulating supercurrents, or vortices, within the array. The interplay of two length scales -the mean separation of vortices and the period of the underlying physical array -gives rise to a wide variety of interesting physical phenomena. Many of these effects show up as variations in the properties of the finite-temperature superconducting phase transitions at different fields. Recent and ongoing experiments have measured the critical exponents in superconducting arrays [3], opening the opportunity to do careful comparison of theory and experiment. In this Letter we examine the critical properties of the 2D XY model for two different values of the magnetic field in the densely frustrated regime (f ≫ 0) and in the presence of disorder.The Hamiltonian of the frustrated XY model iswhere θ j is the phase on site j of a square L × L lattice and A ij = (2π/φ 0 ) j i A · dl is the integral of the vector potential from site i to site j with φ 0 being the flux quantum. The directed sum of the A ij around an elementary plaquette A ij = 2πf where f , measured in the units of φ 0 , is the magnetic flux penetrating each plaquette due to the uniformly applied field. We focus here on the cases f = p/q with p/q = 1/3 and 2/5.A unit cell of the ground state fluxoid pattern for these f is shown in Figure 1(a) [4]. The pattern consists of diagonal stripes composed of a single line of vortices for f = 1 3 and a double line of vortices for f = 2 5 . (A vortex is a plaquette with unit fluxoid occupation, ie. the phase gains 2π when going around the plaquette.) The stripes shown in Figure 1(a) can sit on q sub-lattices, which we associate with members of the Z q group. They can also go along either diagonal, and we associate these two options with members of the Z 2 group. A common speculation for commensurate-incommensurate transitions and the frustrated XY model is that the transition should be in the universality class of the q-state (or 2q-state) Pott's model. We find that this is not the case because domain walls between the different states vary considerably in both energetic and ent...

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confidence: 99%

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confidence: 99%

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confidence: 99%

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Domain Walls and Phase Transitions in the Frustrated Two-DimensionalXYModel

Denniston

Tang²

1997

Phys. Rev. Lett.

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“…The phase transitions for other values of f , e.g., f = 1/3, 2/5, etc., were also discussed in Refs. [42][43][44][45].…”

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confidence: 99%

Finite-temperature phase structures of hard-core bosons in an optical lattice with an effective magnetic field

2012

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We study finite-temperature phase structures of hard-core bosons in a two-dimensional optical lattice subject to an effective magnetic field by employing the gauged CP 1 model. Based on the extensive Monte Carlo simulations, we study their phase structures at finite temperatures for several values of the magnetic flux per plaquette of the lattice and mean particle density. Despite the presence of the particle number fluctuation, the thermodynamic properties are qualitatively similar to those of the frustrated XY model, with only the phase as a dynamical variable. This suggests that cold-atom simulators of the frustrated XY model are available irrespective of the particle filling at each site.

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Equilibrium phase transitions in Josephson junction arrays

Teitel

Complex Behaviour of Glassy Systems

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Phase transitions in the uniformly frustratedXYmodel with frustration parameterf=1/3 studied with use of the microcanonical Monte Carlo technique

Cited by 9 publications

References 14 publications

Domain Walls and Phase Transitions in the Frustrated Two-DimensionalXYModel

Domain Walls and Phase Transitions in the Frustrated Two-DimensionalXYModel

Finite-temperature phase structures of hard-core bosons in an optical lattice with an effective magnetic field

Equilibrium phase transitions in Josephson junction arrays

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