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Quantum Critical Behavior of the Infinite-range Transverse Ising Spin Glass : An Exact Numerical Diagonalization Study

Parongama Sen·Purusattam ray·Bikas K. Chakrabarti
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Abstract

We report exact numerical diagonalization results of the infinite-range Ising spin glass in a transverse field $Γ$ at zero temperature. Eigenvalues and eigenvectors are determined for various strengths of $Γ$ and for system sizes $N \le 16$. We obtain the moments of the distribution of the spin-glass order parameter, the spin-glass susceptibility and the mass gap at different values of $Γ$. The disorder averaging is done typically over 1000 configurations. Our finite size scaling analysis indicates a spin glass transition at $Γ_c \simeq 1.5$. Our estimates for the exponents at the transition are in agreement with those known from other approaches. For the dynamic exponent, we get $z=2.1 \pm 0.1$ which is in contradiction with a recent estimate ($z=4$). Our cumulant analysis indicates the existence of a replica symmetric spin glass phase for $Γ< Γ_c$.

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Parongama Sen, Purusattam ray, Bikas K. Chakrabarti. 1997-05-29. Quantum Critical Behavior of the Infinite-range Transverse Ising Spin Glass : An Exact Numerical Diagonalization Study. https://arxiv.org/abs/cond-mat/9705297

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