## Decay of order in Ising models |

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arbitrary asymptotic decay bulk calculation chapter components consider correlation near free cpr(n critical region crossed bonds cyclic boundary conditions decay of correlation decay of pair decay of spin defined degeneracy degenerate diagonal dimensional dimensions easily eigen eigenstates eigenvectors energy-density correlation functions equal equation exp(-KR expectation value ferromagnet finite field first-order formulae free edges free energy free surfaces Gg(R given gonal high temperatures integral interactions inverse range Ising model labels largest eigenvalue largest level lattice layering direction low temperatures magnetic field matrix elements n-particle n-th nearest-neighbor non-zero field number of spins operators Ornstein-Zernike theory orthonormality pair correlation functions particle band particle number partition function perturbation theory range of correlation saddlepoint second-order single-particle band spectra spin correlation functions subspace tends to infinity tends to zero thermodynamic tion Toeplitz matrix Transfer Matrix treat two-dimensional two-particle vector write zero field zeroth-order