Lower-critical spin-glass dimension from 23 sequenced hierarchical models
The lower-critical dimension for the existence of the Ising spin-glass phase is calculated, numerically exactly, as d[subscript L] = 2.520 for a family of hierarchical lattices, from an essentially exact (correlation coefficent R[superscript 2] = 0.999999) near-linear fit to 23 different diminishing...
Main Authors: | , , |
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Other Authors: | |
Format: | Article |
Language: | English |
Published: |
American Physical Society
2015
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Online Access: | http://hdl.handle.net/1721.1/98229 https://orcid.org/0000-0002-5172-2172 |
Summary: | The lower-critical dimension for the existence of the Ising spin-glass phase is calculated, numerically exactly, as d[subscript L] = 2.520 for a family of hierarchical lattices, from an essentially exact (correlation coefficent R[superscript 2] = 0.999999) near-linear fit to 23 different diminishing fractional dimensions. To obtain this result, the phase transition temperature between the disordered and spin-glass phases, the corresponding critical exponent y[subscript T], and the runaway exponent y[subscript R] of the spin-glass phase are calculated for consecutive hierarchical lattices as dimension is lowered. |
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