In this thesis I have successfully recreated the results that describe the behavior of a transverse-field Ising chain. There is a phase transition when the parameter that controls the influence of the transverse field is one (that is: the factor in front of the transverse-field term and the interaction term are equally big). However, I could not determine exactly what the order parameter should be.\nThen for the transverse-field Ising ladder I have used perturbation theory in the parameter that controls the interaction between the chains. I have found that the phase transition doesn't change position, but that the ground state is a different state compared to the transverse-field Ising chain, when the transverse-field term is smaller than the interaction.In this thesis I have successfully recreated the results that describe the behavior of a transverse-field Ising chain. There is a phase transition when the parameter that controls the influence of the transverse field is one (that is: the factor in front of the transverse-field term and the interaction term are equally big). However, I could not determine exactly what the order parameter should be.\nThen for the transverse-field Ising ladder I have used perturbation theory in the parameter that controls the interaction between the chains. I have found that the phase transition doesn't change position, but that the ground state is a different state compared to the transverse-field Ising chain, when the transverse-field term is smaller than the interaction.

Jan 1, 20190 citations

1次元Random Transverse-Ising Modelの基底状態相転移 (秩序化における乱れと非線型--ヘテロな物理系と量子揺動効果)

仁浅川, Masuo Suzuki

物性研究Aug 1, 19950 citations

Monte Carlo method for the Ising model in a transverse field

Rick J. Creswick, Horácio A. Farach, James M. Knight +1 more

The partition function for the Ising model in a transverse field can be expressed as a sum over the usual Ising states by evaluation of the diagonal matrix elements between Ising states with the use of the cumulant expansion. The cumulant sum is evaluated to all orders in \ensuremath{\beta} and second order in \ensuremath{\Gamma}, the transverse field. The effective Hamiltonian is then employed in Monte Carlo simulation to evaluate the average energy and magnetization in the longitudinal and transverse directions. Comparison with exact results on a one-dimensional chain shows that the method works quite well. Monte Carlo results for the average energy, specific heat, and the transverse and longitudinal components of the magnetization for the transverse Ising model on the simple cubic lattice are presented.The partition function for the Ising model in a transverse field can be expressed as a sum over the usual Ising states by evaluation of the diagonal matrix elements between Ising states with the use of the cumulant expansion. The cumulant sum is evaluated to all orders in \ensuremath{\beta} and second order in \ensuremath{\Gamma}, the transverse field. The effective Hamiltonian is then employed in Monte Carlo simulation to evaluate the average energy and magnetization in the longitudinal and transverse directions. Comparison with exact results on a one-dimensional chain shows that the method works quite well. Monte Carlo results for the average energy, specific heat, and the transverse and longitudinal components of the magnetization for the transverse Ising model on the simple cubic lattice are presented.

Physical review. B, Condensed matterSep 1, 198815 citations

Hitoshi Asakawa, Masuo Suzuki

Aug 20, 19950 citations

仁浅川, Masuo Suzuki

lの基底状態相転移棄大理浅川仁. 鈴木増雄

物性研究Aug 20, 19950 citations

Local dynamics and thermal activation in the transverse-field Ising chain

Jiahao Yang, Weishi Yuan, Takashi Imai +3 more

There has been considerable recent progress in identifying candidate materials for the transverse-field Ising chain (TFIC), a paradigmatic model for quantum criticality. Here, we study the local spin dynamical structure factor of different spin components in the quantum disordered region of the TFIC. We show that the low-frequency local dynamics of the spins in the Ising- and transverse-field directions have strikingly distinctive temperature dependencies. This leads to the thermal-activation gap for the secular term of the nuclear magnetic resonance $1/{T}_{2}^{\ensuremath{'}}$ relaxation rate to be half of that for the $1/{T}_{1}$ relaxation rate. Our findings reveal a surprise in the nonzero-temperature dynamics of the venerable TFIC model and uncover a means to evince the material realization of the TFIC universality.There has been considerable recent progress in identifying candidate materials for the transverse-field Ising chain (TFIC), a paradigmatic model for quantum criticality. Here, we study the local spin dynamical structure factor of different spin components in the quantum disordered region of the TFIC. We show that the low-frequency local dynamics of the spins in the Ising- and transverse-field directions have strikingly distinctive temperature dependencies. This leads to the thermal-activation gap for the secular term of the nuclear magnetic resonance $1/{T}_{2}^{\ensuremath{'}}$ relaxation rate to be half of that for the $1/{T}_{1}$ relaxation rate. Our findings reveal a surprise in the nonzero-temperature dynamics of the venerable TFIC model and uncover a means to evince the material realization of the TFIC universality.

arXiv:2111.15107Physical review. B./Physical review. BSep 29, 202210 citations

1/{T}_{1}

relaxation rate. Our findings reveal a surprise in the nonzero-temperature dynamics of the venerable TFIC model and uncover a means to evince the material realization of the TFIC universality.