Correlation function (statistical mechanics)

（重定向自Correlation length）

Equal-time correlation functions, , as a function of radius for a ferromagnetic spin system above, at, and below at its critical temperature, . Above , exhibits a combined exponential and power-law dependence on distance: . The power-law dependence dominates at distances short relative to the correlation length, , while the exponential dependence dominates at distances large relative to . At , the correlation length diverges, , resulting in solely power-law behavior: . is distinguished by the extreme non-locality of the spatial correlations between microscopic values of the relevant order parameter without long-range order. Below , the spins exhibit spontaneous ordering and thus infinite correlation length. Continuous order-disorder transitions can be understood as the process of the correlation length, , transitioning from being infinite in the low-temperature, ordered state, to finite in a high-temperature, disordered state.

In statistical mechanics, the correlation function is a measure of the order in a system, as characterized by a mathematical correlation function. Correlation functions describe how microscopic variables, such as spin and density, at different positions are related. More specifically, the correlation functions quantifies how microscopic variables co-vary with one another on average across space and time. A classic example of such spatial correlations is in ferro- and antiferromagnetic materials, where the spins prefer to align parallel and antiparallel with their nearest neighbors, respectively. The spatial correlation between spins in such materials is shown in the figure to the right.

单词	Correlation length
释义	Correlation length 英语百科 Correlation function (statistical mechanics) （重定向自Correlation length） In statistical mechanics, the correlation function is a measure of the order in a system, as characterized by a mathematical correlation function. Correlation functions describe how microscopic variables, such as spin and density, at different positions are related. More specifically, the correlation functions quantifies how microscopic variables co-vary with one another on average across space and time. A classic example of such spatial correlations is in ferro- and antiferromagnetic materials, where the spins prefer to align parallel and antiparallel with their nearest neighbors, respectively. The spatial correlation between spins in such materials is shown in the figure to the right.
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