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      Spin glasses in a field: Three and four dimensions as seen from one space dimension

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          Abstract

          We study the existence of a line of transitions of an Ising spin glass in a magnetic field-known as the de Almeida-Thouless line-using one-dimensional power-law diluted Ising spin-glass models. We choose the power-law exponent to have values that approximately correspond to three- and four-dimensional nearest-neighbor systems and perform a detailed finite-size scaling analysis of the data for large linear system sizes, both using a new approach proposed recently [Phys. Rev. Lett. 103, 267201 (2009)], as well as traditional approaches. Our results for the model corresponding to a three-dimensional system are consistent with there being no de Almeida-Thouless line, although the new finite-size scaling approach does not rule one out. For the model corresponding to four space dimensions, the new and traditional finite-size scaling analyses give conflicting results, indicating the need for a better understanding of finite-size scaling of spin glasses in a magnetic field.

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          Equilibrium behavior of the spin-glass ordered phase

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            Critical Behavior of the Three-Dimensional Ising Spin Glass

            We have simulated, using parallel tempering, the three dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice (L=20) has been studied using a dedicated computer (the SUE machine). We have obtained, measuring the correlation length in the critical region, a strong evidence for a second-order finite temperature phase transition ruling out other possible scenarios like a Kosterlitz-Thouless phase transition. Precise values for the \(\nu\) and \(\eta\) critical exponents are also presented.
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              Scaling theory of the ordered phase of spin glasses

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                Author and article information

                Journal
                2012-11-30
                2013-01-18
                Article
                10.1103/PhysRevB.87.024414
                1211.7297
                b5e05924-6c1c-4140-9eb6-e4c1e3426af8

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                Phys. Rev. B 87, 024414 (2013)
                10 pages, 8 figures, loads of fun!
                cond-mat.dis-nn

                Theoretical physics
                Theoretical physics

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