Metastable states in short-ranged p-spin glasses

The mean number (N) of metastable states in higher order short-range spin glasses is estimated analytically using a variational method introduced by Tanaka and Edwards for very large coordination numbers. For lattices with small connectivities, numerical simulations do not show any significant dependence on the relative positions of the interacting spins on the lattice, indicating thus that these systems can be described by a few macroscopic parameters. As an extremely anisotropic model we consider the low autocorrelated binary spin model and we show through numerical simulations that its landscape has an exceptionally large number of local optima.

[1]  P. Stadler,et al.  Landscape Statistics of the Low Autocorrelated Binary String Problem , 2000, cond-mat/0006478.

[2]  P. Stadler,et al.  Random field models for fitness landscapes , 1999 .

[3]  Dieter Beule,et al.  Evolutionary search for low autocorrelated binary sequences , 1998, IEEE Trans. Evol. Comput..

[4]  Peter F. Stadler,et al.  Correlation length, isotropy and meta-stable states , 1997 .

[5]  J. Fontanari,et al.  Landscape statistics of the p-spin Ising model , 1997, cond-mat/9708133.

[6]  P. Stadler.  Landscapes and their correlation functions , 1996 .

[7]  Jennifer Ryan,et al.  The Depth and Width of Local Minima in Discrete Solution Spaces , 1995, Discret. Appl. Math..

[8]  F. Ritort,et al.  Dynamical behaviour of low autocorrelation models , 1994, cond-mat/9407105.

[9]  G. Parisi,et al.  Replica field theory for deterministic models: II. A non-random spin glass with glassy behaviour , 1994, cond-mat/9406074.

[10]  M. Mézard,et al.  Self induced quenched disorder: a model for the glass transition , 1994, cond-mat/9405075.

[11]  G. Parisi,et al.  Replica field theory for deterministic models: I. Binary sequences with low autocorrelation , 1994, hep-th/9405148.

[12]  Peter F. Stadler,et al.  Linear Operators on Correlated Landscapes , 1994 .

[13]  E D Weinberger,et al.  Why some fitness landscapes are fractal. , 1993, Journal of theoretical biology.

[14]  Walter Kern,et al.  On the Depth of Combinatorial Optimization Problems , 1993, Discret. Appl. Math..

[15]  Peter F. Stadler,et al.  Correlation in Landscapes of Combinatorial Optimization Problems , 1992 .

[16]  Alan S. Perelson,et al.  Molecular evolution on rugged landscapes : proteins, RNA and the immune system : the proceedings of the Workshop on Applied Molecular Evolution and the Maturation of the Immune Response, held March, 1989 in Santa Fe, New Mexico , 1991 .

[17]  M. Cieplak,et al.  Metastable states in disordered ferromagnets , 1987 .

[18]  J. Bernasconi.  Low autocorrelation binary sequences : statistical mechanics and configuration space analysis , 1987 .

[19]  E. Gardner,et al.  Metastable states of a spin glass chain at 0 temperature , 1986 .

[20]  Rammile Ettelaie,et al.  Residual entropy and simulated annealing , 1985 .

[21]  M. Mézard,et al.  The simplest spin glass , 1984 .

[22]  Stephen A Roberts,et al.  Metastable states and innocent replica theory in an Ising spin glass , 1981 .

[23]  A. Bray,et al.  Metastable states in spin glasses with short-ranged interactions , 1981 .

[24]  B. Derrida.  Random-Energy Model: Limit of a Family of Disordered Models , 1980 .

[25]  A. Bray,et al.  Metastable states in spin glasses , 1980 .

[26]  MARCEL J. E. GOLAY,et al.  Sieves for low autocorrelation binary sequences , 1977, IEEE Trans. Inf. Theory.

[27]  S. Kirkpatrick,et al.  Solvable Model of a Spin-Glass , 1975 .