Defect energy of infinite-component vector spin glasses

2005/05/05 by L. W. Lee, A. P. Young · 1 citation
Physics and Astronomy · #Complex Network Analysis Techniques #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.72.036124

published as Phys. Rev. E72, 036124 (2005) · 4 pages, 5 figures

arxiv created 2005/05/05 · openalex publication_date 2005/09/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute numerically the zero-temperature defect energy \ensuremathΔE of the vector spin glass in the limit of an infinite number of spin components m, for a range of dimensions 2\ensuremath\leqslantd\ensuremath\leqslant5. Fitting to \ensuremathΔE\ensuremath∼L^\ensuremathθ, where L is the system size, we obtain: \ensuremathθ\ensuremath≃\ensuremath-1.54\phantom\rule0.1em0ex(d=2), \ensuremathθ\ensuremath≃\ensuremath-1.04\phantom\rule0.1em0ex(d=3), \ensuremathθ\ensuremath≃\ensuremath-0.67\phantom\rule0.1em0ex(d=4), and \ensuremathθ\ensuremath≃\ensuremath-0.37\phantom\rule0.1em0ex(d=5). These results show that the lower critical dimension d_l (the dimension where \ensuremathθ changes sign) is significantly higher for m=\ensuremath∞ than for finite m (where 2<d_l<3).

Citations

• Generalized Bose-Einstein Phase Transition in Large-mComponent Spin Glasses

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