Thermalization of Two- and Three-Dimensional Classical Lattices

Understanding how systems achieve thermalization is a fundamental task in statistical physics. This Letter presents both analytical and numerical evidence showing that thermalization can be universally achieved in sufficiently large two- and three-dimensional lattices via weak nonlinear interactions. Thermalization time follows a universal scaling law unaffected by lattice structures, types of interaction potentials, or whether the lattice is ordered or not. Moreover, this study highlights the critical impact of dimensionality and degeneracy on thermalization dynamics.Received 3 August 2022Revised 11 February 2024Accepted 2 May 2024DOI:https://doi.org/10.1103/PhysRevLett.132.217102© 2024 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAnharmonic lattice dynamicsClassical statistical mechanicsNonequilibrium statistical mechanicsPhysical SystemsDisordered systemsHamiltonian systemsLattice models in statistical physicsStatistical Physics & ThermodynamicsCondensed Matter, Materials & Applied PhysicsNonlinear Dynamics