Non-perturbative renormalization-group approach to lattice models

Abstract

The non-perturbative renormalization-group approach is extended to lattice models, considering as an example a ${\varphi }^4$ theory defined on a $d$-dimensional hypercubic lattice. Within a simple approximation for the effective action, we solve the flow equations and obtain the renormalized dispersion $\eps(\q)$ over the whole Brillouin zone of the reciprocal lattice. In the long-distance limit, where the lattice does not matter any more, we reproduce the usual flow equations of the continuum model. We show how the numerical solution of the flow equations can be simplified by expanding the dispersion in a finite number of circular harmonics.

v1) 8 pages, 7 figures, v2) includes a discussion of the Ginzburg scale vs. the lattice scale

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Cited by in corpus (14)

• The nonperturbative functional renormalization group and its applications
• From local to critical fluctuations in lattice models: a non-perturbative renormalization-group approach
• Infrared behavior and spectral function of a Bose superfluid at zero temperature
• Unified picture of superfluidity: From Bogoliubov's approximation to Popov's hydrodynamic theory
• A Non-Perturbative Renormalization Group approach to quantum XY spin models
• On the Validity of the Law of Mass Action in Three-Dimensional Coagulation Processes
• Critical line of the ${\Phi }^4$ theory on a simple cubic lattice in the local potential approximation
• First-order phase transitions in spinor Bose gases and frustrated magnets
• Long-Range and Many-Body Effects in Coagulation Processes
• Critical line of the ${\Phi }^4$ scalar field theory on a 4D cubic lattice in the local potential approximation
• Fluctuation Effects in the Pair-Annihilation Process with Lévy Dynamics
• Physics-informed neural networks for solving functional renormalization group on a lattice
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Exact renormalization group equation for lattice Ginzburg-Landau models adapted to the solution in the local potential approximation