Two-time Green’s function treatment of field-induced quantum criticality of a -dimensional easy-plane ferromagnet with longitudinal uniform interactions

Thermodynamics of the Classical Planar Ferromagnet Close to the Zero-Temperature Critical Point: A Many-Body Approach

“…This result is strictly connected with the shift exponent ψ = 1 and in drastic contrast with the corresponding relation obtained for the QPFM [27,39], which, due to the presence of quantum fluctuations, shows that ψ = d/2. Equation (75) predicts that χ ⊥ ∼ T −1 as T → 0 along the vertical line h = h c , providing the exponent γ T = ψ = 1, in contrast with the quantum result γ T = ψ = d/2 for the QPFM [28,39].…”

“…A relevant feature of the phase diagram for the CPFM is that it appears qualitatively similar to the one found for the QPFM using different approaches: RG [27] and two-time GF method [34,39]. However, for sufficiently low temperatures along the vertical trajectory h = h c , the quantitative difference between the behaviors of the transverse susceptibility, χ ⊥ ∼ T −1 of the CPFM and χ ⊥ ∼ T −d/2 , may play a crucial role to distinguish classical and quantum fluctuations in realistic PFM-like systems.…”

“…Besides, in the regime Q 3 , decreasing T at fixed h > h c , the transverse susceptibility deviates from the one at T = 0 except for a small power law correction as a function of T and h − h c . The latter feature differs crucially from the QPFM scenario where the correction to the (T = 0)-behavior of χ ⊥ is an exponentially small function of T and h − h c [28,39].…”

“…. This spherical-model incorrect result is typical of the Tyablikov-like decoupling also for the quantum model at finite temperature [28,39,40]. When ω 0 /T θ, (69) yields simply ω 0 h − h c (T) which corresponds to the MF exponent γ h = 1.…”

“…now, we can systematically explore the thermodynamics of the CPFM close to the (T = 0)-CP for different values of the dimensionality d of the system. Bearing this in mind, in strict analogy with the quantum case [28,39], in the following subsections we will show the asymptotic solutions of (52) in the classical…”