2011
DOI: 10.1103/physrevlett.107.047203
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Zero- and Low-Temperature Behavior of the Two-Dimensional±JIsing Spin Glass

Abstract: Recently extended precise numerical methods and droplet scaling arguments allow for a coherent picture of the glassy states of two-dimensional Ising spin glasses to be assembled. The length scale at which entropy becomes important and produces "chaos", the extreme sensitivity of the state to temperature, is found to depend on the type of randomness. For the ±J model this length scale dominates the low-temperature specific heat. Although there is a type of universality, some critical exponents do depend on the … Show more

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Cited by 53 publications
(93 citation statements)
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“…The fact that power-law scaling does hold, in the model studied here as well as in the previously studied case with bimodal couplings [24], must reflect a certain "funnel" structure of the energy landscape where the energy and entropy barriers along the walls down to the global minimum increase sufficiently slowly with the system size. This should be a consequence of the droplet picture in the model with bimodal couplings [11], and also in the case of Gaussian couplings one can construct a similar approximate droplet structure [25] that may explain the behavior found here.…”
Section: Discussionmentioning
confidence: 87%
See 2 more Smart Citations
“…The fact that power-law scaling does hold, in the model studied here as well as in the previously studied case with bimodal couplings [24], must reflect a certain "funnel" structure of the energy landscape where the energy and entropy barriers along the walls down to the global minimum increase sufficiently slowly with the system size. This should be a consequence of the droplet picture in the model with bimodal couplings [11], and also in the case of Gaussian couplings one can construct a similar approximate droplet structure [25] that may explain the behavior found here.…”
Section: Discussionmentioning
confidence: 87%
“…However, due to the considerable challenges with MC simulations, especially for large systems at low temperature, there are still significant issues under debate. For example, whether or not the 2DISG with bimodal J = ±1 and Gaussian couplings belong to the same universality class in their equilibrium criticality is still in question [9][10][11][12][13][14]. Undisputed is the fact that the ground-state properties of the two models are different.…”
Section: Introductionmentioning
confidence: 99%
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“…It has been established that for finite lattice size L there can be considered to be two regimes separated by a crossover temperature T * (L), a "ground state plus gap" regime for T < T * (L), and an "effectively continuous energy level" regime for T > T * (L) [10]. In the infinite-L thermodynamic limit (ThL) T * reaches zero because T * (L) drops with increasing L as T * (L) ∼ 1.1(1)L −1/2 [7,11]. In the strict ground-state limit T ≡ 0 and for finite L, the bimodal 2D ISG exponent η has been estimated to be η = 0.210 (23) [12] from transfer-matrix ground-state measurements, η = 0.14(1) from ground-state spin correlations [13] and η = 0.22(1) from non-zero-energy droplet probabilities [14].…”
Section: Introductionmentioning
confidence: 99%
“…This method has been used to measure numerically the chaos exponents for spinglasses on hypercubic lattices [2,6,[14][15][16]. For each type of perturbation δ (magnetic, disorder, temperature), the droplet scaling theory predicts values of the corresponding chaos exponent ζ δ [2,13], as will be recalled below in the text.…”
Section: Cécile Monthus and Thomas Garelmentioning
confidence: 99%