We study surface critical phenomena of the ${\mathit{S}}^{4}$ model having Gaussian randomness. Using the renormalization-group 4-d expansion, we obtain surface critical exponents indicating the decay of the correlation function, ${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\parallel}}}^{\mathrm{random}}$ and ${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\perp}}}^{\mathrm{random}}$, at the random fixed point. These exponents are evaluated for both the ordinary and special transitions up to the second order, and the surface scaling relation ${\mathrm{\ensuremath{\eta}}}^{\mathrm{random}}$=2${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\perp}}}^{\mathrm{random}}$-${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\parallel}}}^{\mathrm{random}}$ is confirmed in this random system. We also confirm the conformal invariance of the real-space correlation function at criticality.We study surface critical phenomena of the ${\mathit{S}}^{4}$ model having Gaussian randomness. Using the renormalization-group 4-d expansion, we obtain surface critical exponents indicating the decay of the correlation function, ${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\parallel}}}^{\mathrm{random}}$ and ${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\perp}}}^{\mathrm{random}}$, at the random fixed point. These exponents are evaluated for both the ordinary and special transitions up to the second order, and the surface scaling relation ${\mathrm{\ensuremath{\eta}}}^{\mathrm{random}}$=2${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\perp}}}^{\mathrm{random}}$-${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\parallel}}}^{\mathrm{random}}$ is confirmed in this random system. We also confirm the conformal invariance of the real-space correlation function at criticality.

Physical review. B, Condensed matterSep 1, 19927 citations

Critical behavior of random surfaces in one dimension

Joseph Polchinski

Nuclear Physics BDec 1, 1990129 citations

Random‐Field Correlations and Quantum Critical Phenomena

Dimo I. Uzunov, Elka Korutcheva, YONKO T. MILLEV

Abstract The effect of quenched random fields on the zero‐temperature critical behaviour is studied by the means of the Wilson‐Fisher renormalisation‐group recursion relations to first order in the ϵ‐expansion. A number of quantum models is considered. The simultaneous influence of both, the random‐field and the classical‐to‐quantum dimensional crossover phenomena on the quantum critical behaviour is investigated. A special attention is paid to the properties of some reasonable particular forms of Gaussian random correlations which might be of relevance to the description of natural systems.Abstract The effect of quenched random fields on the zero‐temperature critical behaviour is studied by the means of the Wilson‐Fisher renormalisation‐group recursion relations to first order in the ϵ‐expansion. A number of quantum models is considered. The simultaneous influence of both, the random‐field and the classical‐to‐quantum dimensional crossover phenomena on the quantum critical behaviour is investigated. A special attention is paid to the properties of some reasonable particular forms of Gaussian random correlations which might be of relevance to the description of natural systems.

physica status solidi (b)Jul 1, 19857 citations

Effect of Second-Rank Random Anisotropy on Critical Phenomena of Random Field O(N) Spin Model

Yoshinori Sakamoto, Hisamitsu Mukaida, Chigak Itoi

We study the critical behavior of a random field O(N ) spin model included a second-rank random anisotropy term in spatial dimensions 4 < d < 6, by means of the replica method and the 1/N -expansion.We assume the replica symmetry, and study the stability of replica symmetric saddle point against the fluctuation due to the second-rank random anisotropy.Consequently, the replica symmetric saddle point is shown to be stable in the large N limit.Thus, the dimensional reduction holds in the large N limit.We study the critical behavior of a random field O(N ) spin model included a second-rank random anisotropy term in spatial dimensions 4 < d < 6, by means of the replica method and the 1/N -expansion.We assume the replica symmetry, and study the stability of replica symmetric saddle point against the fluctuation due to the second-rank random anisotropy.Consequently, the replica symmetric saddle point is shown to be stable in the large N limit.Thus, the dimensional reduction holds in the large N limit.

Progress of Theoretical Physics SupplementJan 1, 20051 citation

We study surface critical phenomena of the

{\mathit{S}}^{4}

model having Gaussian randomness. Using the renormalization-group 4-d expansion, we obtain surface critical exponents indicating the decay of the correlation function, ${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\parallel}}}^{\mathrm{random}}$ and ${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\perp}}}^{\mathrm{random}}$, at the random fixed point. These exponents are evaluated for both the ordinary and special transitions up to the second order, and the surface scaling relation ${\mathrm{\ensuremath{\eta}}}^{\mathrm{random}}$=2${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\perp}}}^{\mathrm{random}}$-${\mathrm{\ensuremath{\eta}}}_{\mathrm{\ensuremath{\parallel}}}^{\mathrm{random}}$ is confirmed in this random system. We also confirm the conformal invariance of the real-space correlation function at criticality.