Finite spin fluctuations

In summary, we showed that near a FQCP, spin fluctuation exchange gives rise to a strong first order transition into a triplet superconducting state. As a result, Tc saturates at a nonzero value at criticality. The first order transition persists up to a finite distance from the FQCP, where it becomes second order. 

Up to now, we have concentrated on the physics at zero kelvin. In this section, we extend the studies to finite temperatures and discuss finite temperature phase diagrams. The physics at finite temperatures is dominated by thermal fluctuations between low lying excited states of the system. These fluctuations can include spin fluctuations, fluctuations between different valence states, or fluctuations between different orbitally ordered states, if present. Such fluctuations can be addressed througih a so-called alloy analogy. If there is a timescale that is slow compared to the motion of the valence electrons, and on which the configurations persist between the system fluctuations, one can replace the temporal average over all fluctuations by an ensemble average over all possible (spatially... 

Fig. 6. Paramagnetic critical scattering in La2Cu04. Energy-integrating scans across the two-dimensional rod of scattering measure the Fourier transform of the instantaneous spin-spin correlation function in La2Cu04 above T. The peak width (corrected for finite instrumental resolution) is the inverse correlation length for antiferromagnetic spin fluctuations. The dashed lines show the experimental resolution function, and the solid lines are the results of fits to a Lorentzian lineshape convolved with the resolution for three different temperatures. From Kcimer et al. (1992).

For the sake of clarity we shall first discuss in Section 6.2.1 ground-state properties in the framework of the unrestricted Hartree-Fock approximation. In Section 6.2.2 the theory is extended to finite temperatures by using a functional integral formalism including spin fluctuations. Finally, in Section 6.2.3 we analyze the problem of electron correlations by exact diagonalization of the simpler single-band Hubbard model. 

Magnetic Properties at Finite Temperatures Spin-Fluctuation Effects... 

The impact of this is tremendous. No long-range order (LRO) can exist at finite temperature in one dimension no crystals, no magnets, no superconductors. Only special transitions are possible in two dimensions. The Ising model (n = 1 component) is an example [7]. The Kosterlitz-Thouless transition [8], without LRO, is another case for d = 2 and n = 2, discussed in Section V.C. The thermal fluctuations are very destructive in lower dimensions. Quantum fluctuations (i.e., those associated with the dynamics of a system) also tend to suppress LRO and can sometimes destroy it even at 0 K when the Mermin-Wagner theorem does not apply. Such is the case of the quantum spin- antiferromagnetic models [9] in one dimension. 

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