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A Realistic Model for a Spin Glass

  • James A. Given (a1) and George Stell (a1)

Abstract

We develop exact integral equations satisfied by the spin-spin correlation functions of a realistic spin glass model. This is done by considering the magnetic particles in a spin glass to be bound states of hard sphere ‘atoms’ and classical ‘spins’, the former of which are quenched in position, while the latter are allowed to equilibrate. We develop the replica Ornstein-Zernike (ROZ) equations, which are satisfied by the correlation functions of such a partly quenched mixture. We prove that two widely used OZ closures, the Percus-Yevick approximation and mean-spherical approximation are indifferent to quenched disorder, i.e., they give tihe same results for quenched and for fully annealed systems. We extend the ROZ equations to apply to the spin glass by using the proper interaction-site formalism. Preliminary numerical results are discussed.

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[1] Madden, W.A. and Glandt, E.D., J. Stat. Phys. 51, 537 (1988)
[2] Given, J., “Liquid-State Methods for Random Media: I. Random Sequential Absorption”, Phys. Rev. A45, 816 (1992)
[3] Given, J., “Liquid-State Methods for Random Media: II. Spin Glasses”, J. Chem. Phys. 96, 2287 (1992)
[4] Høye, J.S. and Stell, G., Phys. Rev. Lett 36, 1569 (1976)
[5] Martimia, E. and Stell, G., J. Stat. Phys. 27, 407 (1982)
[6] Stratt, R.M., J. Chem. Phys. 80, 5764 (1984); J. Chem. Phys. 77, 2108 (1982)
[7] Chandler, D. and Pratt, L.R., J. Chem. Phys. 69, 2925 (1976)
[8] Høye, J. and Stell, G., J. Chem. Phys. 88, 7061 (1978)

A Realistic Model for a Spin Glass

  • James A. Given (a1) and George Stell (a1)

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