Stationary correlations for a far-from-equilibrium spin chain

Abstract

A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even ͑odd͒ lattice sites experience a temperature T e (T o ). Detailed balance is violated so that the spin chain settles into a nonequilibrium stationary state, characterized by multiple interactions of increasing range and spin order. We derive the equations of motion for arbitrary correlation functions and solve them to obtain an exact representation of the steady state. Two nontrivial amplitudes reflect the sublattice symmetries; otherwise, correlations decay exponentially, modulo the periodicity of the ring. In the long-chain limit, they factorize into products of two-point functions, in precise analogy to the equilibrium Ising chain. The exact solution confirms the expectation, based on simulations and renormalization group arguments, that the longtime, long-distance behavior of this two-temperature model is Ising-like, in spite of the apparent complexity of the stationary distribution.

Thermal contact through a two-temperature kinetic Ising chain

“…The latter formulae are compatible with the expressions of the stationary two-spin correlations determined in Ref. [2] in the case where ν o = ν e .…”

“…By mapping to the dynamics of spin domain walls and using free fermion techniques, we determine the scaled generating function for the cumulants of the exchanged heat amounts per unit of time in the long time limit.1 In Ref.[5] the terminology "generalized" detailed balance is used. 2 We notice that the first requirement is not satisfied by the Ising chain model of Ref.[7], where two thermostats at different temperatures act on every spin : the latter model does not describe a situation of thermal contact.…”

Nonequilibrium statistical mechanics of a two-temperature Ising ring with conserved dynamics

“…Nearly all studies involve dynamics which are (essentially) translationally invariant, while many involve anisotropy. There are a number of examples of work being done on systems coupling the two baths to every spin or every other spin (for Glauber dynamics in d ≥ 1) [28][29][30][31][32][33][34][35][36]. In the case of the alternating coupling, the two dimensional model was found to exhibit an order-disorder phase transition that belonged to the Ising universality class.…”

Large Deviation Functional of the Weakly Asymmetric Exclusion Process

“…The study of steady states of non-equilibrium systems has motivated a lot of works over the last decades [1][2][3][4][5][6][7][8][9]. It is now well established that non-equilibrium systems exhibit in general long-range correlations in their steady state [4,[10][11][12].…”