Lyapunov instabilities in lattices of interacting classical spins at infinite temperature

Abstract

Abstract. We numerically investigate Lyapunov instabilities for one-, two-and three-dimensional lattices of interacting classical spins at infinite temperature. We obtain the largest Lyapunov exponents for a very large variety of nearestneighbor spin-spin interactions and complete Lyapunov spectra in a few selected cases. We investigate the dependence of the largest Lyapunov exponents and whole Lyapunov spectra on the lattice size and find that both quickly become size-independent. Finally, we analyze the dependence of the largest Lyapunov exponents on the anisotropy of spin-spin interaction with the particular focus on the difference between bipartite and nonbipartite lattices.

Chaotic properties of spin lattices near second-order phase transitions

“…The initial conditions corresponding to a given value of the total energy of the system are selected using the routine described in Ref. 18 , which draws them from a uniform distribution of the energy shell.…”

Classical spin simulations with a quantum two-spin correction

“…It was also shown analytically in Ref. [15], that, in the limit of the infinite number of interacting neighbours, correlation functions C(t) computed classically and quantum-mechanically become identical -consequence of the fact that commutators for quantum spins and Poisson brackets for classical spins have essentially the same structure [39,47] and, as a result, lead to the same expressions for the time derivatives of C(t).…”

Estimating ergodization time of a chaotic many-particle system from a time reversal of equilibrium noise

“…It is supported by the extensive numerical experience, e.g. [14][15][16][17], showing that the eigenvectors corresponding to max l exhibit rather erratic behavior. The above factorization leads to Appendix B. Derivation of equation (8) Here we derive equation…”

“…Various aspects of this work are relevant to the previous investigations of lattice gauge models [9][10][11][12][13] and spin lattice models [14][15][16][17]. We also note that our method involves the classical counterpart of out-of-timeorder quantum correlators (OTOCs) [18] that have been actively investigated in recent years in the context of quantum thermalization [19][20][21][22][23] and many-body localization problems [24][25][26][27][28][29].…”