An effective mean-field theory based on cumulant expansion is expanded to deal with the first-order transition of the Potts model on general d-dimensional hypercubic lattice in this paper. It is a generalized mean-field method developed from the cumulant expansion of average free energy. As we shall see, it gives the traditional mean-field result at its first-order approximation and the effective mean field introduced by this method will be amended with the approximation's order increasing. For a full view of this method, we have carried out calculations up to the seventh-order approximation on a square $(d=2)$ lattice since some known exact quantites of this case are terminals that should be approached. The results show this method has the potential to be a useful tool to calculate thermodynamical observables of spin systems.An effective mean-field theory based on cumulant expansion is expanded to deal with the first-order transition of the Potts model on general d-dimensional hypercubic lattice in this paper. It is a generalized mean-field method developed from the cumulant expansion of average free energy. As we shall see, it gives the traditional mean-field result at its first-order approximation and the effective mean field introduced by this method will be amended with the approximation's order increasing. For a full view of this method, we have carried out calculations up to the seventh-order approximation on a square $(d=2)$ lattice since some known exact quantites of this case are terminals that should be approached. The results show this method has the potential to be a useful tool to calculate thermodynamical observables of spin systems.

Physical review. B, Condensed matterMar 7, 20012 citations

Worldline Monte Carlo method for few-body nuclear physics

Shailesh Chandrasekharan A, Son T. Nguyen, Thomas R. Richardson

In this work we introduce a worldline-based fermion Monte Carlo algorithm for studying few body quantum mechanics of self-interacting fermions in the Hamiltonian lattice formulation. Our motivation to construct the method comes from our interest in studying renormalization of chiral nuclear effective-field theory with lattice regularization. In particular we wish to apply our method to compute the lattice spacing dependence of local lattice interactions as we take the continuum limit of the lattice theory. Our algorithm can compute matrix elements of the operator $exp(\ensuremath{-}\ensuremath{\beta}H)$, where $H$ is the lattice Hamiltonian and $\ensuremath{\beta}$ is a free real parameter. These elements help us compute deep bound states that are well separated from scattering states even at values of $\ensuremath{\beta}$ which are not very large. Computing these bound-state energies accurately can help us study renormalization of the lattice theory. In addition to developing the algorithm, in this work we also introduce a finite-volume renormalization scheme for the lattice Hamiltonian of the leading pionless effective-field theory and show how it would work in the one- and two-body sectors.In this work we introduce a worldline-based fermion Monte Carlo algorithm for studying few body quantum mechanics of self-interacting fermions in the Hamiltonian lattice formulation. Our motivation to construct the method comes from our interest in studying renormalization of chiral nuclear effective-field theory with lattice regularization. In particular we wish to apply our method to compute the lattice spacing dependence of local lattice interactions as we take the continuum limit of the lattice theory. Our algorithm can compute matrix elements of the operator $exp(\ensuremath{-}\ensuremath{\beta}H)$, where $H$ is the lattice Hamiltonian and $\ensuremath{\beta}$ is a free real parameter. These elements help us compute deep bound states that are well separated from scattering states even at values of $\ensuremath{\beta}$ which are not very large. Computing these bound-state energies accurately can help us study renormalization of the lattice theory. In addition to developing the algorithm, in this work we also introduce a finite-volume renormalization scheme for the lattice Hamiltonian of the leading pionless effective-field theory and show how it would work in the one- and two-body sectors.

arXiv:2402.15377Physical Review CAug 14, 20244 citations

Effective field theory

CO-PUBLISHED WITH IMPERIAL COLLEGE PRESS eBooksSep 1, 20040 citations

(d=2)

lattice since some known exact quantites of this case are terminals that should be approached. The results show this method has the potential to be a useful tool to calculate thermodynamical observables of spin systems.

H

is the lattice Hamiltonian and $\ensuremath{\beta}$ is a free real parameter. These elements help us compute deep bound states that are well separated from scattering states even at values of $\ensuremath{\beta}$ which are not very large. Computing these bound-state energies accurately can help us study renormalization of the lattice theory. In addition to developing the algorithm, in this work we also introduce a finite-volume renormalization scheme for the lattice Hamiltonian of the leading pionless effective-field theory and show how it would work in the one- and two-body sectors.