The method of Mermin and Wagner [Phys. Rev. Lett. 17, 1133 (1966)] is used to show that one- and two-dimensional spin systems interacting with a general isotropic interaction H=12 ∑ ijn Iij(n) (Si·Sj)n,where the exchange interactionsIij(n) are of finite range, cannot order in the sense that 〈Oi〉=0for all traceless operators Oi defined at a single site i. Mermin and Wagner have proved the above for the case n = 1 with Oi = Si, i.e., for the Heisenberg Hamiltonian. The proof allows us to rule out the possibility that a small isotropic biquadratic exchange (Si·Sj)2 could induce ferromagnetism or antiferromagnetism in a two-dimensional Heisenberg system.
Here we examine O(n) systems with arbitrary two spin interactions (of unspecified range) within a general framework. We shall focus on translationally invariant interactions. In the this case, we determine the ground states of the
O(n≥2) systems. We further illustrate how one may establish Peierls bounds for many Ising systems with long range interactions. We study the effect of thermal fluctuations on the ground states and derive the corresponding fluctuation integrals. The study of the thermal fluctuation spectra will lead us to discover a very interesting odd-even
n (coupling-decoupling) effect. We will prove a generalized Mermin-Wagner-Coleman theorem for all two dimensional systems (of arbitrary range) with analytic kernels in
k space. We will show that many three dimensional systems have smectic like thermodynamics. We will examine the topology of the ground state manifolds for both translationally invariant and spin glass systems. We conclude with a discussion of O(n) spin dynamics in the general case.
Using an asymmetric two-leg ladder comprising pairing and metallic chains, this Letter proves the striking power of reservoir-mediated boosting of superconductivity. Using many-body numerics on large systems at zero and finite temperature, we unravel the processes by which the metal parameters can impact the effective pairing strength and the ranged pair-pair coupling mediated by the metal. These then enhance key superconducting properties far above those of the isolated system. Thus, our Letter identifies a general mechanism by which reservoirs can strongly suppress the effects of the Mermin-Wagner theorem in finite-sized systems, allowing even large one-dimensional systems to appear practically ordered.