# A new effective-field technique for the ferromagnetic spin-1 Blume-Capel model in a transverse crystal field

## TL;DR

This paper introduces a novel effective-field technique for analyzing the quantum ferromagnetic spin-1 Blume-Capel model with a transverse crystal field, improving phase diagram accuracy and capturing quantum phase transitions.

## Contribution

The paper develops a new approximating method using finite clusters and non-interacting spins, enhancing phase diagram accuracy and computational efficiency for the model.

## Key findings

- Qualitatively correct phase diagram with proper first-order line behavior
- Identification of quantum phase transitions due to transverse anisotropy
- Advantage of larger cluster sizes in the proposed method

## Abstract

A new approximating technique is developed so as to study the quantum ferromagnetic spin-1 Blume-Capel model in the presence of a transverse crystal field in the square lattice. Our proposal consists of approaching the spin system by considering islands of finite clusters whose frontiers are surrounded by non-interacting spins that are treated by the effective-field theory. The resulting phase diagram is qualitatively correct, in contrast to most effective-field treatments, in which the first-order line exhibits spurious behavior by not being perpendicular to the anisotropy axis at low temperatures. The effect of the transverse anisotropy is also verified by the presence of quantum phase transitions. The possibility of using larger sizes constitutes an advantage to other approaches where the implementation of larger sizes is costly computationally.