Скачать или смотреть The Edwards-Anderson model in a tube​ - Isodoro Gonzales-Adalid Permartin - Young Seminars SIFS

Abstract: The lower critical dimension, d_c^-, marks the threshold dimension that sustains a finite-temperature phase transition from those that do not [1]. Within the Replica Symmetry Broken (RSB) framework, d_c^- approximately 2.5 for the Ising Edwards-Anderson model [1-4]. In this scenario, a three-dimensional spin glass (which should have a glassy phase below the critical temperature because D=3 is larger than 2.5) exhibits a surprising behavior in a tubular geometry: correlations along the tube axis decay exponentially with distance, no matter how small the temperature is. In fact, a Wilsonian Renormalization Group (WRG) [5] analysis reveals that a one-dimensional fixed point governs the system behavior. Starting from previous results obtained by Franz, Parisi, and Virasoro [2], we forecast that the correlation length in such geometries scales with the transverse size L as L^(4/3). We have tested this prediction through large-scale Monte Carlo simulations, utilizing more than 400000 GPU hours and reaching lattices of up to 24x24x88. Remarkably, the tubular geometry enables the implementation of an efficient cluster algorithm based on Houdayer trick [6], accelerating equilibration even for the largest systems. Moreover, by employing Open Boundary Conditions along the long axis, we can reduce finite-size corrections and accurately extract the correlation length from comparatively shorter systems. Our numerical results show excellent agreement with the predicted L^(4/3) scaling. This provides direct numerical evidence that the RSB theoretical framework correctly describes the finite-size scaling of the correlations in this quasi-one-dimensional regime.

References

[1] G. Parisi, Statistical Field Theory (Addison-Wesley, Redwood City, 1988).
[2] S. Franz, G. Parisi, and M.A. Virasoro. Interfaces and lower critical dimension in a spin glass model. J Phys (France) (1994) 4:1657-67. doi:10.1051/jp1:1994213
[3] S. Boettcher. Stiffness of the Edwards-Anderson Model in all Dimensions. Phys. Rev. Lett. 95, 197205 (2005). doi:10.1103/PhysRevLett.95.197205
[4] A. Maiorano and G. Parisi. Support for the value 5/2 for the spin glass lower critical dimension at zero magnetic field. Proc Natl Acad Sci U S A (2018) 115:5129-34. doi:10.1073/pnas.1720832115
[5] See, for instance, J. Cardy, Scaling and Renormalization in Statistical Physics (Cambridge University Press, 1996).
[6] J. Houdayer. A cluster Monte Carlo algorithm for 2-dimensional spin glasses. The European Physical Journal B, vol. 22, no. 4 (2001), p. 479-484. doi:10.1007/PL00011151

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