Abstract To gain a deeper understanding of the glassy phase in p-spin quantum models, this paper examines the dynamics of the N-vector x ∈ R N through the framework of renormalization group (RG) theory. First, we focus on perturbation theory, which is more suitable than nonperturbative techniques due to the specific temporal non-locality of the model after disorder integration. We compute the one-loop β-function and explore the structure of its fixed points. Next, we develop the nonperturbative RG approach based on the standard Wetterich–Morris formalism, using two approximation schemes to address the model’s non-locality. We investigate the vertex expansion in the symmetric phase and assess the reliability of the approximations for the fixed-point solutions. Finally, we extend our analysis beyond the symmetric phase by using an expansion around the vacuum of the local potential. Our numerical investigations particularly focus on the cases p = 2 and p = 3.Abstract To gain a deeper understanding of the glassy phase in p-spin quantum models, this paper examines the dynamics of the N-vector x ∈ R N through the framework of renormalization group (RG) theory. First, we focus on perturbation theory, which is more suitable than nonperturbative techniques due to the specific temporal non-locality of the model after disorder integration. We compute the one-loop β-function and explore the structure of its fixed points. Next, we develop the nonperturbative RG approach based on the standard Wetterich–Morris formalism, using two approximation schemes to address the model’s non-locality. We investigate the vertex expansion in the symmetric phase and assess the reliability of the approximations for the fixed-point solutions. Finally, we extend our analysis beyond the symmetric phase by using an expansion around the vacuum of the local potential. Our numerical investigations particularly focus on the cases p = 2 and p = 3.

arXiv:2412.17600Journal of Statistical Mechanics Theory and ExperimentSep 1, 20251 citation

Renormalization group and quantum critical phenomena in the large-n limit

Gaetano Busiello, L. De Cesare, Ileana Rabuffo

Physica A Statistical Mechanics and its ApplicationsFeb 1, 198341 citations

Quantum crossover behaviour of the N-vector model in the large-N limit

Katarzyna Walasek

Physica A Statistical Mechanics and its ApplicationsJul 1, 19861 citation

Pokrovsky-Talapov model at finite temperature: A renormalization-group analysis

Achilleas Lazarides, O. Tieleman, C. Morais Smith

We calculate the finite-temperature shift of the critical wave vector ${Q}_{c}$ of the Pokrovsky-Talapov model using a renormalization-group analysis. Separating the Hamiltonian into a part that is renormalized and one that is not, we obtain the flow equations for the stiffness and an arbitrary potential. We then specialize to the case of a cosine potential, and compare our results to well-known results for the sine-Gordon model, to which our model reduces in the limit of vanishing driving wave vector $Q=0$ . Our results may be applied to describe the commensurate-incommensurate phase transition in several physical systems and allow for a more realistic comparison with experiments, which are always carried out at a finite temperature.We calculate the finite-temperature shift of the critical wave vector ${Q}_{c}$ of the Pokrovsky-Talapov model using a renormalization-group analysis. Separating the Hamiltonian into a part that is renormalized and one that is not, we obtain the flow equations for the stiffness and an arbitrary potential. We then specialize to the case of a cosine potential, and compare our results to well-known results for the sine-Gordon model, to which our model reduces in the limit of vanishing driving wave vector $Q=0$. Our results may be applied to describe the commensurate-incommensurate phase transition in several physical systems and allow for a more realistic comparison with experiments, which are always carried out at a finite temperature.

arXiv:0909.0526Physical Review BDec 15, 20099 citations

Renormalization Group Equation for Critical Phenomena

Franz Wegner, Anthony Houghton

An exact renormalization equation is derived by making an infinitesimal change in the cutoff in momentum space. From this equation the expansion for critical exponents around dimensionality 4 and the limit $n=\ensuremath{\infty}$ of the $n$ -vector model are calculated. We obtain agreement with the results of Wilson and Fisher, and with the spherical model.An exact renormalization equation is derived by making an infinitesimal change in the cutoff in momentum space. From this equation the expansion for critical exponents around dimensionality 4 and the limit $n=\ensuremath{\infty}$ of the $n$-vector model are calculated. We obtain agreement with the results of Wilson and Fisher, and with the spherical model.

Physical Review AJul 1, 1973729 citations

Renormalization groups and variational states in an interacting 1D quantum model

Stefan Rommer

Jan 1, 19960 citations

We calculate the finite-temperature shift of the critical wave vector

{Q}_{c}

of the Pokrovsky-Talapov model using a renormalization-group analysis. Separating the Hamiltonian into a part that is renormalized and one that is not, we obtain the flow equations for the stiffness and an arbitrary potential. We then specialize to the case of a cosine potential, and compare our results to well-known results for the sine-Gordon model, to which our model reduces in the limit of vanishing driving wave vector

Q=0

. Our results may be applied to describe the commensurate-incommensurate phase transition in several physical systems and allow for a more realistic comparison with experiments, which are always carried out at a finite temperature.

n

-vector model are calculated. We obtain agreement with the results of Wilson and Fisher, and with the spherical model.