Phase diagram of gauge glasses

Ozeki, Yukiyasu; Nishimori, Hidetoshi

doi:10.1088/0305-4470/26/14/009

Cited by 83 publications

(134 citation statements)

References 54 publications

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“…21) These results are generalized to a wider class of systems including the usual Ising SG and the Z q and XY gauge glasses. 22) Although the gauge theory provides us with surprising results, its targets have so far been limited to classical spin systems. In the present paper, we generalize this theory so that it applies to quantum spin systems.…”

Section: Introductionmentioning

confidence: 99%

Gauge Theory for Quantum Spin Glasses

2006

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The gauge theory for random spin systems is extended to quantum spin glasses to derive a number of exact and/or rigorous results. The transverse Ising model and the quantum gauge glass are shown to be gauge invariant. For these models, an identity is proved that the expectation value of the gauge invariant operator in the ferromagnetic limit is equal to the one in the classical equilibrium state on the Nishimori line. As a result, a set of inequalities for the correlation function are proved, which restrict the location of the ordered phase. It is also proved that there is no long-range order in the two-dimensional quantum gauge glass in the ground state. The phase diagram for the quantum XY Mattis model is determined.

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Section: Introductionmentioning

confidence: 99%

Gauge Theory for Quantum Spin Glasses

2006

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“…On the other hand, Carpentier and Le Doussal [20,21] have proposed a renormalization group (RG) method to analyze strong disorder features at low temperatures of the XY gauge glass model [22,23,24,25,26,27]. Introducing higher charge fugacities, they have derived generalized RG equations for the Coulomb gas model, which is remarkably intimate relationship with a nonlinear diffusion equation called KPP equation [28,29,30].…”

Section: Introductionmentioning

confidence: 99%

Random hopping fermions on bipartite lattices: density of states, inverse participation ratios, and their correlations in a strong disorder regime

Yamada¹,

Fukui²

2004

Nuclear Physics B

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We study Anderson localization of non-interacting random hopping fermions on bipartite lattices in two dimensions, focusing our attention to strong disorder features of the model. We concentrate ourselves on specific models with a linear dispersion in the vicinity of the band center, which can be described by a Dirac fermion in the continuum limit. Based on the recent renormalization group method developed by Carpentier and Le Doussal for the XY gauge glass model, we calculate the density of states, inverse participation ratios, and their spatial correlations. It turns out that their behavior is quite different from those expected within naive weak disorder approaches.

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“…The case (1.2) corresponds to a situation where the average magnetic flux over each elementary plaquette of the grain network is an integer multiple of Φ 0 , but random displacement of superconducting grains from a perfect lattice structure yields quenched random phase shifts [7,11]. On the theoretical side, model (1.1) and its variants have been studied extensively in the past [5,[12][13][14][15][16][17][18][19]. Result of previous studies can be summarized as follows.…”

Section: Introductionmentioning

confidence: 99%

Vortex statistics in a disordered two-dimensionalXYmodel

Tang

1996

Phys. Rev. B

109

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The equilibrium behavior of vortices in the classical two-dimensional (2D) XY model with uncorrelated random phase shifts is investigated. The model describes Josephson-Junction arrays with positional disorder, and has ramifications in a number of other bond-disordered 2D systems. The vortex Hamiltonian is that of a Coulomb gas in a background of quenched random dipoles, which is capable of forming either a dielectric insulator or a plasma. We confirm a recent suggestion by Nattermann, Scheidl, Korshunov, and Li [J. Phys. I (France) 5, 565 (1995)], and by Cha and Fertig [Phys. Rev. Lett. 74, 4867 (1995)] that, when the variance σ of random phase shifts is smaller than a critical value σc, the system is in a phase with quasi-long-range order at low temperatures, without a reentrance transition. This conclusion is reached through a nearly exact calculation of the single-vortex free energy, and a Kosterlitz-type renormalization group analysis of screening and random polarization effects from vortex-antivortex pairs. The critical strength of disorder σc is found not to be universal, but generally lies in the range 0 < σc < π/8. Argument is presented to suggest that the system at σ > σc does not possess long-range glassy order at any finite temperature. In the ordered phase, vortex pairs undergo a series of spatial and angular localization processes as the temperature is lowered. This behavior, which is common to many glass-forming systems, can be quantified through approximate mappings to the random energy model and to the directed polymer on the Cayley tree. Various critical properties at the order-disorder transition are calculated.75.10. Nr, 64.60.Ak, 74.50.+r, 74.60.Ge

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Phase diagram of gauge glasses

Cited by 83 publications

References 54 publications

Gauge Theory for Quantum Spin Glasses

Gauge Theory for Quantum Spin Glasses

Random hopping fermions on bipartite lattices: density of states, inverse participation ratios, and their correlations in a strong disorder regime

Vortex statistics in a disordered two-dimensionalXYmodel

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