Spin correlation length

An alternative way to describe the phenomenon is to consider that the ground state of a chain is already divided into domains at any temperatures. In order for the system to follow a small variation of the magnetic field some domains have to reverse their spin orientation. This occurs through a random walk of the DWs, that is, equal probability for the DW to move backward or forward, which implies that the DW needs a time proportional to d2 to reach the other end of a domain of length d. Given that d scales as the two spins correlation length, ., which, for the Ising model, is proportional to exp(2///rB7 ), for unitary spins, the same exponential relaxation is found... 

The RR s can also be used to compute the spin correlator (Si. Sj) which has an exponential decay behaviour exp(- / — j / ), with the spin correlation length which satisfies the equation... 

Figure 2.55 Left The appearance of asymmetric Warren line shape peaks with decreasing temperature for Li2Mn204, indicative of two-dimensional spin correlations. Right The temperature dependence of the spin-spin correlation length showing an abrupt, first-order like increase below 60 Reprinted with...

This relation between the spin correlation length and the hole concentration has been experimentally observed in La2-. Sr tCu04 [67]. The spin gap grows with doping and, as follows from self-consistent calculations [55], with temperature. 

In other words the H -h OH correlation depends strictly on the shape of the triatomic and not just on the three bond lengths treated as independent variables. It is in this sense that the restriction (54) on Vj introduces an approximation to the potential. In effect by making it we are allowing for the spin correlation rules but not spatial correlation rules. 

A spin ladder is an array of coupled spin chains. The horizontal chains are called the legs, the vertical ones, rungs. In the case of spin one-half antiferromagnet spin-ladders, these systems show a. remarkable behaviour in function of the number of leg there is a gap in the excitation spectrum of even-leg ladders and, on the contrary, no gap in the excitation spectrum of odd-leg ladders. In terms of correlation lengths, this means that there is short (long) -range spin correlation in even (odd) -legladder (see [24] for a review). 

According to Eqs.(42) the spin correlations have an exponential decay and the correlation length rc is... 

Our results suggest that the spin correlation functions decay exponentially with a correlation length 1 for an arbitrary parameter a. We also assume that the decay of the correlation function is of the exponential type for the 14 parameter model as well, i.e., for any choice of site spinor I>A/u/p. This assumption is supported in special cases 1) the partition of the system into one-dimensional chains with exactly known exponentially decaying correlation functions 2) the two-dimensional AKLT model, for which the exponential character of the decay of the correlation function has been rigorously proved [32], Further evidence of the stated assumption lies in the numerical results obtained for various values of the parameter in the one-parameter model. 

Now, when spin-spin correlations are not neglected, there should exist a temperature below which a phase transition to a more organized state will occur. If this state is characterized by order on an infinite length scale (i.e. the length scale of the correlations is essentially the dimension of the sample) this is known as long-range order (LRO). The transition that occurs is analogous to the condensation of a gas to form a crystalline solid. We are not concerned here with a detailed discussion of the voluminous literature on phase transitions of this type (also known as critical phenomena). 

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