Non-perturbative effects in spin glasses

Scientific Reports
Michele Castellana, Giorgio Parisi

Abstract

We present a numerical study of an Ising spin glass with hierarchical interactions--the hierarchical Edwards-Anderson model with an external magnetic field (HEA). We study the model with Monte Carlo (MC) simulations in the mean-field (MF) and non-mean-field (NMF) regions corresponding to d ≥ 4 and d < 4 for the d-dimensional ferromagnetic Ising model respectively. We compare the MC results with those of a renormalization-group (RG) study where the critical fixed point is treated as a perturbation of the MF one, along the same lines as in the -expansion for the Ising model. The MC and the RG method agree in the MF region, predicting the existence of a transition and compatible values of the critical exponents. Conversely, the two approaches markedly disagree in the NMF case, where the MC data indicates a transition, while the RG analysis predicts that no perturbative critical fixed point exists. Also, the MC estimate of the critical exponent ν in the NMF region is about twice as large as its classical value, even if the analog of the system dimension is within only ~2% from its upper-critical-dimension value. Taken together, these results indicate that the transition in the NMF region is governed by strong non-perturbative effects.

References

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Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Michele Castellana, Giorgio Parisi
May 24, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Michele Castellana, Giorgio Parisi
Apr 12, 2012·Proceedings of the National Academy of Sciences of the United States of America·Raquel Alvarez BañosDavid Yllanes

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Citations

Apr 15, 2016·Physical Review. E·T AspelmeierJoonhyun Yeo

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