Numerical studies on critical properties of the Kosterlitz-Thouless phase for the gauge glass model in two dimensions

Ozeki, Yukiyasu; Yotsuyanagi, Satoshi; Sakai, Takahisa; Echinaka, Yuki

doi:10.1103/physreve.89.022122

Cited by 6 publications

(9 citation statements)

References 67 publications

(100 reference statements)

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“…On the other hand, since the flow from ρ 4 = 1 can end in the infrared onto any point of the line (18), also the disordered model should exhibit a BKT phase, and this is confirmed by numerical studies (see e.g. [24,25]). The phase diagram observed in these studies is similar to that of Fig.…”

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confidence: 63%

“…1, with the ferromagnetic phase replaced by the BKT phase 3 . On the other hand, numerical studies still disagree on the values of critical exponents along the portion of the phase boundary going from the multicritical point M to the critical point of the pure model: a constant magnetic exponent η = 1/4 (the value at the BKT transition in the pure model) was deduced in [24], while a continuously varying η was found in [25].…”

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confidence: 98%

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Exact results for the O(N ) model with quenched disorder

Delfino¹,

Lamsen²

2018

J. High Energ. Phys.

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We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points for O(N )-symmetric models with quenched disorder in two dimensions. Random fixed points are characterized by two disorder parameters: a modulus that vanishes when approaching the pure case, and a phase angle. The critical lines fall into three classes depending on the values of the disorder modulus. Besides the class corresponding to the pure case, a second class has maximal value of the disorder modulus and includes Nishimori-like multicritical points as well as zero temperature fixed points. The third class contains critical lines that interpolate, as N varies, between the first two classes. For positive N , it contains a single line of infrared fixed points spanning the values of N from √ 2 − 1 to 1. The symmetry sector of the energy density operator is superuniversal (i.e. N -independent) along this line. For N = 2 a line of fixed points exists only in the pure case, but accounts also for the Berezinskii-Kosterlitz-Thouless phase observed in presence of disorder.

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confidence: 63%

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confidence: 98%

Exact results for the O(N ) model with quenched disorder

Delfino¹,

Lamsen²

2018

J. High Energ. Phys.

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“…The effect of a finite amount of phase disorder has been studied in some detail: Extensive work on randomphase XY (RPXY) models [13][14][15][16][17][18][19][20][21][22][23][24] -without frustrationhas established 15,22 that the ground state has QLRO with power-law correlations at small disorder; this state continuously connects to the QLRO phase at finite T . Upon increasing the disorder strength a KT-like transition destroys the QLRO phase in favor of a disordered phase with exponentially decaying correlations.…”

Section: Frustrated Xy Models and Random-phase Disordermentioning

confidence: 99%

“…The critical disorder strength decreases with increasing temperature. While it was initially argued from perturbative considerations 13 that a re-entrant behavior might be observed where the dependence of critical disorder strength for the KT transition is non-monotonic with temperature and at zero temperature the critical disorder strength vanishes, non-perturbative treatments [15][16][17]19,21 and Monte-Carlo (MC) simulations [22][23][24] have shown that the RPXY model does not exhibit any re-entrant behavior and the QLRO phase survives upto a finite critical value of disorder strength even at T = 0.…”

Section: Frustrated Xy Models and Random-phase Disordermentioning

confidence: 99%

“…[10][11][12] The effect of quenched disorder has mainly been studied in the (unfrustrated) superconductor context: While random couplings do not change the physics qualitatively, random phases do: At T = 0, LRO is destroyed in favor QLRO by infinitesimally small phase disorder, while large disorder leads to short-range-ordered state. [13][14][15][16][17][18][19][20][21][22][23][24] In contrast, the effect of randomness in the context of frustrated easy-plane magnets has not been studied in much detail. This is a particularly interesting topic given that recent work has shown that bond disorder in two-dimensional non-collinear magnets is able to destroy T = 0 LRO via effective dipolar random fields.…”

Section: Introductionmentioning

confidence: 99%

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Random-bond disorder in two-dimensional non-collinear XY antiferromagnets: From quasi-long-range order to spin glass

Dey,

Andrade,

Vojta

2020

Preprint

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We study effects of quenched bond disorder in frustrated easy-plane antiferromagnets in two space dimensions, using a combination of analytical and numerical techniques. We consider local-moment systems which display non-collinear long-range order at zero temperature, with the antiferromagnetic triangular-lattice XY model as a prime example. We show that (i) weak bond disorder transforms the clean ground state into a state with quasi-long-range order, and (ii) strong bond disorder results in a short-range-ordered glassy ground state. Using extensive Monte Carlo simulations, we also track the fate of the quasi-long-range-ordered phase at finite temperature and the associated Kosterlitz-Thouless-like transition. Making contact with previous studies of disordered XY models, we discuss similarities and differences concerning the interplay of disorder and frustration. Our results are also of relevance to non-collinear Heisenberg magnets in an external magnetic field.

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Critical lines in the pure and disordered O(N) model

Delfino¹,

Lamsen²

2019

J. Stat. Mech.

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We consider replicated O(N ) symmetry in two dimensions within the exact framework of scale invariant scattering theory and determine the lines of renormalization group fixed points in the limit of zero replicas corresponding to quenched disorder. A global pattern emerges in which the different critical lines are located within the same parameter space. Within the subspace corresponding to the pure case (no disorder) we show how the critical lines for non-intersecting loops (−2 ≤ N ≤ 2) are connected to the zero temperature critical line (N > 2) via the BKT line at N = 2. Disorder introduces two more parameters, one of which vanishes in the pure limit and is maximal for the solutions corresponding to Nishimori-like and zero temperature critical lines. Emergent superuniversality (i.e. N -independence) of some critical exponents in the disordered case and disorder driven renormalization group flows are also discussed.For the permutational symmetry S q , characteristic of the q-state Potts model, this exploration was performed in [6] and revealed new results. In particular, the maximal value of q allowing for a fixed point was found to be 1 5.56.., instead of the previously expected value 4. This leaves room for a second order phase transition in a q = 5 antiferromagnet for which lattice candidates exist [8,9]. A line of fixed points with q = 3 and central charge 1 was also predicted for which a lattice realization has recently been found [10].A further, particularly remarkable feature of the scale invariant scattering formalism in two dimensions is that it extends to the problem of quenched disorder [11], i.e. to those "random" fixed points that had seemed out of reach for exact methods. In particular, for the random bond Potts model it was then possible to see analytically for the first time the softening of the phase transition by disorder above q = 4 [11], a phenomenon expected on rigorous grounds [12] (see also [13]). Quite unexpected was instead the emergence of a mechanism allowing for the q-independence of the correlation length critical exponent ν, with the magnetization exponent β remaining q-dependent [11]. This phenomenon of partial superuniversality finally accounts for the evidence emerged from a variety of investigations [14,15,16,17,18,19,20,21,22] that ν does not show any appreciable deviation from the value 1 up to q = ∞.Recently [23] we have shown how the scale invariant scattering approach can be applied to the O(N ) vector model with quenched disorder and gives global and exact access to a pattern of fixed points that previously had been the object of perturbative (for weak disorder) [24] and numerical [25] studies. In this paper we give all the solutions of the fixed point equations (table 1 below) and discuss their physical properties. In particular, we show how the critical lines parametrized by N are located with respect to each other in the space of parameters. This is interesting already for the case without disorder ("pure"), for which we exhibit how the passage from the critical lines fo...

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Numerical studies on critical properties of the Kosterlitz-Thouless phase for the gauge glass model in two dimensions

Cited by 6 publications

References 67 publications

Exact results for the O(N ) model with quenched disorder

Exact results for the O(N ) model with quenched disorder

Random-bond disorder in two-dimensional non-collinear XY antiferromagnets: From quasi-long-range order to spin glass

Critical lines in the pure and disordered O(N) model

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