Abstract
We explore the low-temperature thermodynamic properties and crossovers of ad-dimensional classical planar Heisenberg ferromagnet in a longitudinal magnetic field close to its field-induced zero-temperature critical point by employing the two-time Green’s function formalism in classical statistical mechanics. By means of a classical Callen-like method for the magnetization and the Tyablikov-like decoupling procedure, we obtain, for anyd, a low-temperature critical scenario which is quite similar to the one found for the quantum counterpart. Remarkably, ford>2the discrimination between the two cases is found to be related to the different values of the shift exponent which governs the behavior of the critical line in the vicinity of the zero-temperature critical point. The observation of different values of the shift-exponent and of the related critical exponents along thermodynamic paths within the typical V-shaped region in the phase diagram may be interpreted as a signature of emerging quantum critical fluctuations.
Highlights
An intriguing aspect of quantum phase transitions (QPTs) [1] is that quantum critical fluctuations may play a relevant role at finite temperature
The emerging idea was that, to single out conventional quantum criticality, it is not sufficient to observe a power-law behavior of the correlation length or susceptibility decreasing temperature towards zero in the Vshaped quantum critical region of the phase diagram [1]; rather, the accurate determination of the critical exponents becomes the key ingredient to decide if we are in the influence domain of the quantum critical point (QCP) or the physics is governed by thermal fluctuations
In the present paper we have explored the low-temperature properties of the d-dimensional classical planar ferromagnet (CPFM), which exhibits a field-induced zero-temperature critical point, by adopting the two-time Green’s function framework in classical statistical mechanics
Summary
An intriguing aspect of quantum phase transitions (QPTs) [1] is that quantum critical fluctuations may play a relevant role at finite temperature. The Wilson RG [26, 27], applied to a suitable functional representation of the spin-1/2 PFM, capturing the essential low-temperature physics, and the two-time Green’s function technique [28], utilized to investigate the microscopic spin-S model, have provided a reliable scenario of the global phase diagram and crossovers in the vicinity of the QCP. We will use the two-time Green’s function method in classical statistical mechanics [29], developed and tested in [30,31,32,33], on microscopic classical spin model This allows us to perform in parallel the quantum [28] and the classical analysis for any d, giving a transparent relation between the CPFM and the spin-S QPFM, both exhibiting a zerotemperature critical point. For utility of reader, Appendix A is devoted to an outline of the two-time Green’s function framework in classical statistical mechanics and Appendix B presents a method, alternative to the one employed in [22], to obtain the magnetization as the solution of the Callen-like method
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