Statistical mechanics of a nonlinear relaxation process: Equilibrium properties

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Abstract
We have studied a spin-1/2 system interacting with a classical stochastic oscillator in the overdamped regime, simulating a thermal bath. Our aim is to understand the influence of the reaction field, i.e., the effect of the dipole on its bath, which is usually neglected in the current treatments. We have faced the problem of the role of this reaction field with the help of computer simulation. We found that the trajectories of the dipole x component exhibit behaviors suggesting that, in some range of the parameters of the system, the model should have a bistable character. Moreover, the average equilibrium value of the dipole along the z axis shows a significant deviation from the ‘‘weak-coupling predictions’’ of either classical or quantum statistical mechanics. We have explained all these properties via a renormalization procedure which, in the strong-coupling regime, makes the Hamiltonian of interest very different from the bare Hamiltonian. Among other things, this renormalized Hamiltonian leads to a bimodal distribution for the energy, in excellent agreement with the numerical simulations.