2008/01/02 by S. M. Ali Tabei, S. M. A Tabei, Michel J. P. Gingras +5
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Condensed matter physics #Dipole #Hamiltonian (control theory) #Ising model #Mathematical physics #Mathematics #Monte Carlo method #Phase (matter) #Phase diagram #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Monte Carlo #Quantum mechanics #Quantum phase transition #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.other #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.78.184408
published as Phys. Rev. B 78, 184408 (2008) · 22 pages, 14 figures
arxiv created 2008/01/02 · openalex publication_date 2008/11/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Results from a recent quantum Monte Carlo (QMC) study [P. B. Chakraborty et al., Phys. Rev. B 70, 144411 (2004)] of a model of the LiHoF4 Ising magnetic material in an external transverse magnetic field, Bx, show a discrepancy with experimental results, even for small Bx where quantum fluctuations are small. This discrepancy persists asymptotically close to the classical ferromagnet to paramagnet phase transition. In this paper, we numerically reinvestigate the temperature T versus transverse-field phase diagram of LiHoF4 in the regime of weak Bx. In this regime, starting from an effective low-energy spin-1/2 description of LiHoF4, we apply a cumulant expansion to derive an effective temperature-dependent classical Hamiltonian that incorporates perturbatively the small quantum fluctuations in the vicinity of the classical phase transition at Bx=0. Via this effective classical Hamiltonian, we study the Bx\text\ensuremath-T phase diagram via classical Monte Carlo simulations. In particular, we investigate the influence on the phase diagram of various effects that may be at the source of the discrepancy between the previous QMC results and the experimental ones. In particular, we consider two different ways of handling the long-range dipole-dipole interactions and explore how the Bx\text\ensuremath-T phase diagram is modified when using different microscopic crystal-field Hamiltonians. The main conclusion of our work is that we fully reproduce the previous QMC results at small Bx. Unfortunately, none of the modifications to the microscopic Hamiltonian that we explore are able to provide a Bx\text\ensuremath-T phase diagram compatible with the experiments in the quasiclassical small Bx regime.