Physical review. B, Condensed matter

Quantump-state Potts spin glass in a transverse field: Dynamical correlations and first-order phase transition

T. K. Kopeć, G. Büttner

Published Jul 1, 1992• 0 citations

Abstract

The p-component quantum Potts spin-glass model is considered in the mean-field approximation via the thermofield-dynamics (TFD) method. Quantum effects appear as the action of a transverse field \ensuremath{\Gamma} which represents the tunneling frequency between different discrete Potts states. Applying the Sherrington-Kirkpatrick infinite-interaction-range scheme in the TFD formalism, we find a continuous spin-glass transition for p\ensuremath{\le}6 and discontinuous for p>6 at the field-dependent critical line ${\mathit{T}}_{\mathit{c}}$(\ensuremath{\Gamma}), as demonstrated in the jump of the temperature dependence of the spin-glass order parameter. Interestingly, in contrast to the statics the dynamical theory leads to a continuous slowing down as ${\mathit{T}}_{\mathit{c}}$(\ensuremath{\Gamma}) is approached from the ergodic side, indicating the existence of the infinitely-long-lived metastable states.

DOI: 10.1103/physrevb.46.1015

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Physical review. B, Condensed matter

Quantump-state Potts spin glass in a transverse field: Dynamical correlations and first-order phase transition

T. K. Kopeć, G. Büttner

Published Jul 1, 1992• 0 citations

Publisher

Abstract

{\mathit{T}}_{\mathit{c}}

(\ensuremath{\Gamma}), as demonstrated in the jump of the temperature dependence of the spin-glass order parameter. Interestingly, in contrast to the statics the dynamical theory leads to a continuous slowing down as

{\mathit{T}}_{\mathit{c}}

(\ensuremath{\Gamma}) is approached from the ergodic side, indicating the existence of the infinitely-long-lived metastable states.

DOI: 10.1103/physrevb.46.1015

Related papers

Quantump-state Potts spin glass: Transverse-field effects and freezing transition

T. K. Kopeć, G. Büttner

The p-component quantum Potts spin-glass model is considered in the mean-field approximation via the thermo-field-dynamics method. Quantum effects appear as the action of a transverse field \ensuremath{\Gamma} that represents the tunneling frequency between different discrete Potts states. Applying the Sherrington-Kirkpatrick infinite-range-interaction scheme, we estimate the spin-glass phase boundary in the temperature-field (T-\ensuremath{\Gamma}) plane. We find that the transverse field tends to decrease the transition temperature ${\mathit{T}}_{\mathit{c}}$ (\ensuremath{\Gamma}). However, it turns out that with an increasing number of states p, a pronounced nonmonotonic temperature dependence of ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{c}}$(T) appears, resulting in a reentrant behavior in the low-temperature region.The p-component quantum Potts spin-glass model is considered in the mean-field approximation via the thermo-field-dynamics method. Quantum effects appear as the action of a transverse field \ensuremath{\Gamma} that represents the tunneling frequency between different discrete Potts states. Applying the Sherrington-Kirkpatrick infinite-range-interaction scheme, we estimate the spin-glass phase boundary in the temperature-field (T-\ensuremath{\Gamma}) plane. We find that the transverse field tends to decrease the transition temperature ${\mathit{T}}_{\mathit{c}}$(\ensuremath{\Gamma}). However, it turns out that with an increasing number of states p, a pronounced nonmonotonic temperature dependence of ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{c}}$(T) appears, resulting in a reentrant behavior in the low-temperature region.

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Infinite-range Ising spin glass with a transverse field under the static approximation

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In this paper we investigate for the infinite-range Ising spin-glass model [i.e., the Sherrington-Kirkpatrick (SK) model] with a transverse field under the static approximation by using the imaginary-time replica formalism. From the investigations we show three important results: First, we show that a replica-symmetric quantum spin-glass phase is stable in most of the area of the spin-glass phase in the temperature-transverse field phase diagram. This confirms the existence of a stable replica-symmetric spin glass phase under the static approximation, which is contrary to some previous results derived without the static approximation where the replica-symmetric solution is always unstable in the whole spin-glass phase. Second, we show our theoretical result for the nonlinear susceptibility ${\ensuremath{\chi}}_{\mathrm{nl}}$ which conforms to the experimental result of nonlinear susceptibility measurement by Wu et al. [Phys. Rev. Lett. 71, 1919 (1993)] in a quantum spin glass ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}.$ Third, in a classical (SK) spin-glass system, we confirm the anomaly in the second temperature derivative of ${C}_{H}/T$ near the glass transition temperature ${T}_{g},$ associated possibly with the field-dependent variation of entropy in the spin glass transition, which agrees with the previous experimental observation in a classical spin glass system CuMn by Fogle et al. [Phys. Rev. Lett. 50, 1815 (1983)]. We also show that this anomaly is suppressed by the nonzero transverse field of the quantum spin glass system, by which we can check for the quantum tunneling competing against spin freezing.In this paper we investigate for the infinite-range Ising spin-glass model [i.e., the Sherrington-Kirkpatrick (SK) model] with a transverse field under the static approximation by using the imaginary-time replica formalism. From the investigations we show three important results: First, we show that a replica-symmetric quantum spin-glass phase is stable in most of the area of the spin-glass phase in the temperature-transverse field phase diagram. This confirms the existence of a stable replica-symmetric spin glass phase under the static approximation, which is contrary to some previous results derived without the static approximation where the replica-symmetric solution is always unstable in the whole spin-glass phase. Second, we show our theoretical result for the nonlinear susceptibility ${\ensuremath{\chi}}_{\mathrm{nl}}$ which conforms to the experimental result of nonlinear susceptibility measurement by Wu et al. [Phys. Rev. Lett. 71, 1919 (1993)] in a quantum spin glass ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}.$ Third, in a classical (SK) spin-glass system, we confirm the anomaly in the second temperature derivative of ${C}_{H}/T$ near the glass transition temperature ${T}_{g},$ associated possibly with the field-dependent variation of entropy in the spin glass transition, which agrees with the previous experimental observation in a classical spin glass system CuMn by Fogle et al. [Phys. Rev. Lett. 50, 1815 (1983)]. We also show that this anomaly is suppressed by the nonzero transverse field of the quantum spin glass system, by which we can check for the quantum tunneling competing against spin freezing.

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Physical review. B, Condensed matterJun 1, 198945 citations

Quantum vector spin-glass models in an applied field

Yadin Y. Goldschmidt, Pik-Yin Lai

We use the static approximation to investigate the phase diagram of the infinite-ranged quantum Heisenberg spin glass (QHSG) in an external field, as well as the phase diagram of a two-component quantum spin glass (QXYSG) in a transverse or a longitudinal field. For the QHSG we find that, for strong field (H) and low temperature (T), the phase transition into the spin-glass phase characterized by nonzero transverse spin-glass ordering is given by ${\mathit{T}}_{\mathit{c}}$ \ensuremath{\sim}exp[- ${\mathit{H}}^{2}$ /(2 ${\mathit{J}}^{2}$ ${\mathit{S}}^{2}$ )], as compared with ${\mathit{T}}_{\mathit{c}}$ \ensuremath{\sim}exp{- ${\mathit{H}}^{2}$ /[2 ${\mathit{J}}^{2}$ S(S+1)]} for classical spins of magnitude \ensuremath{\surd}S(S+1) . In the case of QXYSG in a transverse field (\ensuremath{\Gamma}), the phase boundary terminates at \ensuremath{\Gamma}/J=2 for T=0.We use the static approximation to investigate the phase diagram of the infinite-ranged quantum Heisenberg spin glass (QHSG) in an external field, as well as the phase diagram of a two-component quantum spin glass (QXYSG) in a transverse or a longitudinal field. For the QHSG we find that, for strong field (H) and low temperature (T), the phase transition into the spin-glass phase characterized by nonzero transverse spin-glass ordering is given by ${\mathit{T}}_{\mathit{c}}$\ensuremath{\sim}exp[-${\mathit{H}}^{2}$/(2${\mathit{J}}^{2}$${\mathit{S}}^{2}$)], as compared with ${\mathit{T}}_{\mathit{c}}$\ensuremath{\sim}exp{-${\mathit{H}}^{2}$/[2${\mathit{J}}^{2}$S(S+1)]} for classical spins of magnitude \ensuremath{\surd}S(S+1) . In the case of QXYSG in a transverse field (\ensuremath{\Gamma}), the phase boundary terminates at \ensuremath{\Gamma}/J=2 for T=0.

Physical review. B, Condensed matterMay 1, 199117 citations

{\mathit{T}}_{\mathit{c}}

{\mathit{T}}_{\mathit{c}}

(\ensuremath{\Gamma}) is approached from the ergodic side, indicating the existence of the infinitely-long-lived metastable states.

{\mathit{T}}_{\mathit{c}}

(\ensuremath{\Gamma}). However, it turns out that with an increasing number of states p, a pronounced nonmonotonic temperature dependence of ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{c}}$(T) appears, resulting in a reentrant behavior in the low-temperature region.

{C}_{H}/T

near the glass transition temperature

{T}_{g},

associated possibly with the field-dependent variation of entropy in the spin glass transition, which agrees with the previous experimental observation in a classical spin glass system CuMn by Fogle et al. [Phys. Rev. Lett. 50, 1815 (1983)]. We also show that this anomaly is suppressed by the nonzero transverse field of the quantum spin glass system, by which we can check for the quantum tunneling competing against spin freezing.

The infinite-range quantum Ising spin glass in transverse ($\ensuremath{\Gamma}$) and longitudinal (

h

) fields is studied by means of thermo-field-dynamics as a substitute for the

n

-replica trick. With the use of a one-loop approximation for the dynamic self-interaction the stability of the mean-field-type solution against the action of fluctuations is investigated in the parameter space (${k}_{B}T, \ensuremath{\Gamma}, h$).

{\mathit{T}}_{\mathit{c}}

\ensuremath{\sim}exp[-

{\mathit{H}}^{2}

/(2

{\mathit{J}}^{2}

{\mathit{S}}^{2}

)], as compared with

{\mathit{T}}_{\mathit{c}}

\ensuremath{\sim}exp{-

{\mathit{H}}^{2}

/[2

{\mathit{J}}^{2}

S(S+1)]} for classical spins of magnitude \ensuremath{\surd}S(S+1) . In the case of QXYSG in a transverse field (\ensuremath{\Gamma}), the phase boundary terminates at \ensuremath{\Gamma}/J=2 for T=0.