%0 Journal Article %1 glauber1963timedependent %A Glauber, Roy J. %D 1963 %J Journal of Mathematical Physics %K Glauber_dynamics Ising_model interacting_particle_systems original statistical_physics %N 2 %T Time‐Dependent Statistics of the Ising Model %U http://dx.doi.org/10.1063/1.1703954 %V 4 %X The individual spins of the Ising model are assumed to interact with an external agency (e.g., a heat reservoir) which causes them to change their states randomly with time. Coupling between the spins is introduced through the assumption that the transition probabilities for anyone spin depend on the ".a~ues of the neighboring ~I?in:" This dependence is determined, in part, by the detailed balancing condItion obeyed by the equihbnum state of the model. The Markoff process which describes the spin functions is analyzed in detail for the case of a closed N-member chain. The expectation values of the individual spins and of the products of pairs of spins, each of the pair evaluated at a different are found explicitly. The influence of a uniform, time-varying magnetic field upon the model IS dIscussed, and the frequency-dependent magnetic susceptibility is found in the weak-field limit. Some fluctuation-dissipation theorems are derived which relate the susceptibility to the Fourier transform of the time-dependent correlation function of the magnetization at equilibrium.

@article{glauber1963timedependent, abstract = {The individual spins of the Ising model are assumed to interact with an external agency (e.g., a heat reservoir) which causes them to change their states randomly with time. Coupling between the spins is introduced through the assumption that the transition probabilities for anyone spin depend on the ".a~ues of the neighboring ~I?in:" This dependence is determined, in part, by the detailed balancing condItion obeyed by the equihbnum state of the model. The Markoff process which describes the spin functions is analyzed in detail for the case of a closed N-member chain. The expectation values of the individual spins and of the products of pairs of spins, each of the pair evaluated at a different are found explicitly. The influence of a uniform, time-varying magnetic field upon the model IS dIscussed, and the frequency-dependent magnetic susceptibility is found in the weak-field limit. Some fluctuation-dissipation theorems are derived which relate the susceptibility to the Fourier transform of the time-dependent correlation function of the magnetization at equilibrium.}, added-at = {2014-05-28T15:19:52.000+0200}, author = {Glauber, Roy J.}, biburl = {https://www.bibsonomy.org/bibtex/246a1d52c892bf2a5412ecba00b726d6d/peter.ralph}, interhash = {8bc58a3da0ad9face5f9b6275ccc8ed4}, intrahash = {46a1d52c892bf2a5412ecba00b726d6d}, journal = {Journal of Mathematical Physics}, keywords = {Glauber_dynamics Ising_model interacting_particle_systems original statistical_physics}, number = 2, timestamp = {2014-05-28T15:24:34.000+0200}, title = {Time‐Dependent Statistics of the Ising Model}, url = {http://dx.doi.org/10.1063/1.1703954}, volume = 4, year = 1963 }