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تسجيل مستخدم جديدOnsager algebra and cluster XY-models in a transverse magnetic field
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تأليف
Jacques H.H. Perk
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The correlation functions of certain $n$-cluster XY models are explicitly expressed in terms of those of the standard Ising chain in transverse field.
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In this paper we analize a family of one dimensional fully analytically solvable models, named the n-cluster models in a transverse magnetic field, in which a many-body cluster interaction competes with a uniform transverse magnetic field. These mode
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tuations 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 LiHoF$_4$ in the regime of weak $B_x$. In this regime, starting from an effective low-energy spin-1/2 description of LiHoF$_4$, 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 $B_x=0$. Via this effective classical Hamiltonian, we study the $B_x-T$ 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. For example, we consider two different ways of handling the long-range dipole-dipole interactions and explore how the $B_x-T$ 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 $B_x$. Unfortunately, none of the modifications to the microscopic Hamiltonian that we explore are able to provide a $B_x-T$ phase diagram compatible with the experiments in the small semi-classical $B_x$ regime.
We study the fidelity susceptibility in the two-dimensional(2D) transverse field Ising model and the 2D XXZ model numerically. It is found that in both models, the fidelity susceptibility as a function of the driving parameter diverges at the critica
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