Rigorous bounds of the Lyapunov exponents of the one-dimensional random Ising model

Journal Article · Sat Jul 01 04:00:00 EDT 1995 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/BF02178363· OSTI ID:468300

Pasquini, M; Paladin, G; Serva, M ^[1]

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1. Universita dell`Aquila, L`Aquila (Italy)

We find analytic upper and lower bounds of the Lyapunov exponents of the product of random matrices related to the one-dimensional disordered Ising model, using a deterministic map which transforms the original system into a new one with smaller average couplings and magnetic fields. The iteration of the map gives bounds which estimate the Lyapunov exponents with increasing accuracy. We prove, in fact, that both the upper and the lower bounds converge to the Lyapunov exponents in the limit of infinite iterations of the map. A formal expression of the Lyapunov exponents is thus obtained in terms of the limit of a sequence. Our results allow us to introduce a new numerical procedure for the computation of the Lyapunov exponents which has a precision higher than Monte Carlo simulations.

• Sponsoring Organization: USDOE
• OSTI ID: 468300
• Journal Information: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 1-2 Vol. 80; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
COMPUTERIZED SIMULATION
HAMILTONIANS
ISING MODEL
LYAPUNOV METHOD
NUMERICAL ANALYSIS
RANDOMNESS
TRANSFER MATRIX METHOD