On the interplay of classical and quantum fluctuations: an exactly solvable model for a structural phase transition

Finite-size scaling investigations in the quantum varphi4-model with long-range interaction

“…Though derived for the special case of the ϕ 4 model with long-range interaction in the large n limit, the obtained here results are expected to hold also for many other cases. For example, recently, a model suitable to handle the joint description of classical and quantum fluctuations in an exact manner, was considered in a number of publications [20,[26][27][28][29][30]. This model is a modification of the ϕ 4 -lattice model used extensively in the investigation of the critical behaviour of the the structural phase transitions [31], in the spirit of the self-consistent phonon approximation method [26].…”

Theory of a spherical-quantum-rotors model: Low-temperature regime and finite-size scaling

“…Equations of the type ͑3.1͒ are specific for a closed-form approximation ͑in the d-dimensional case͒ in the theory of phase transitions. They reflect the availability of spherical constraints 11,[20][21][22] or self-consistent equations [26][27][28][29] and so generate similar critical behavior for various physical phenomena. The central role of this type of equations can be confirmed by a more sophisticated large-n limit analysis.…”

“…frequently used in the theory of structural phase transitions (see Refs. [23][24][25][26]. So the Hamiltonian (2.1) can be thought as a simple but rather general model to test some analytical and numerical techniques in the theory of magnetic and structural phase transitions.…”

“…directly to the anharmonic crystal model see Refs. [23][24][25][26] and it can also provide a methodology for seeking different quantum finite-size effects in such systems.…”

“…Earlier a class of exactly solvable lattice models intended to study the displacive structural phase transition have been intensively considered in both finite-size and bulk geometry. [26][27][28][29] The main feature of these models is that the real anharmonic interaction is substituted with its quantum mean spherical approximation reducing the problem to an exactly solvable one. We expect that the analytical technique proposed below will apply to these models too.…”