Yoshiki Matsuda et al 2008 J. Phys. A: Math. Theor. 41 324012 doi:10.1088/1751-8113/41/32/324012
The distribution of Lee–Yang zeros and Griffiths singularities in the ±J model of spin glasses
Yoshiki Matsuda1, Hidetoshi Nishimori1 and Koji Hukushima2
Show affiliationsWe investigate the distribution of zeros of the partition function of the two- and three-dimensional symmetric ±J Ising spin glasses on the complex field plane. We use the method to analytically implement the idea of a numerical transfer matrix which provides us with the exact expression of the partition function as a polynomial of fugacity. The results show that zeros are distributed in a wide region in the complex field plane. Nevertheless, we observe that zeros on the imaginary axis play dominant roles in the critical behaviour since zeros on the imaginary axis are in closer proximity to the real axis. We estimate the density of zeros on the imaginary axis by an importance-sampling Monte Carlo algorithm, which enables us to sample very rare events. Our result suggests that the density has an essential singularity at the origin. This observation is consistent with the existence of Griffiths singularities in the present systems. This is the first evidence for Griffiths singularities in spin glass systems in equilibrium.
- PACS
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75.10.Nr Spin-glass and other random models
75.50.Lk Spin glasses and other random magnets
75.30.Kz Magnetic phase boundaries (including magnetic transitions, metamagnetism, etc.)
- MSC
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82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
82D30 Random media, disordered materials (including liquid crystals and spin glasses)
- Subjects
- Dates
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Issue 32 (15 August 2008)
Received 19 December 2007, in final form 13 February 2008
Published 30 July 2008
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The distribution of Lee–Yang zeros and Griffiths singularities in the ±J model of spin glasses
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