Multi-interaction mean-field renormalization group

TL;DR

This paper extends the mean-field renormalization group method to handle complex Hamiltonians with multiple interactions, accurately modeling systems like Ising models with second-neighbor couplings and interacting surface morphologies.

Contribution

It introduces a generalized renormalization approach that accounts for multiple interaction types without arbitrary truncations, improving modeling accuracy.

Findings

Accurate results for 2D and 3D Ising models with second-neighbor interactions.

Successful application to a morphological surface model.

No arbitrary truncations in the renormalization process.

Abstract

We present an extension of the previously proposed mean-field renormalization method to model Hamiltonians which are characterized by more than just one type of interaction. The method rests on scaling assumptions about the magnetization of different sublattices of the given lattice and it generates as many flow equations as coupling constants without arbitrary truncations on the renormalized Hamiltonian. We obtain good results for the test case of Ising systems with an additional second-neighbor coupling in two and three dimensions. An application of the method is also done to a morphological model of interacting surfaces introduced recenlty by Likos, Mecke and Wagner [J. Chem. Phys. {\bf{102}}, 9350 (1995)]. PACS: 64.60.Ak, 64.60.Fr, 05.70.Jk