%0 Book Section %1 statphys23_0162 %A Obuchi, T. %A Nishimori, H. %A Sherrington, D. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K diagram effects glass interaction phase quantum spin statphys23 topic-9 %T Phase diagram of the $p$-spin-interacting spin glass with ferromagnetic bias and a transverse field in the infinite-$p$ limit %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=162 %X We study the $p$-spin interacting spin glass in a transverse field in the large-$p$ limit. Our purpose is to investigate three competing effects; quenched disorder, ferromagnetic bias, and quantum fluctuations. Although this model has already been studied by some researchers, we have extended their results and succeeded in clarifying some new properties. By using the Trotter decomposition, this quantum system is reduced to a corresponding classical system. The replica method is applied to the classical system and the equations of state are derived by the saddle-point method. Due to quantum effects, order parameters become dependent on time (Trotter index) and the equations are highly complex. We avoid the problem by employing the static approximation and analytically obtain the free energy and order parameters in the limit $p ınfty$. The resultant phase diagram consists of four phases; the classical and quantum paramagnetic, ferromagnetic, and spin glass phases. In addition, we examine the validity of the static approximation by the large-$p$ expansion taking into account the time-dependent corrections in the ferromagnetic phase. In the classical paramagnetic and spin glass phases, it is known that the static approximation is valid and order parameters do not depend on times as long as $p$ is sufficiently large. For the ferromagnetic phase, our calculations show similar results to that of the two phases. Meanwhile, in the quantum paramagnetic phase, it is known that an order parameter is time-dependent and thermodynamic quantities violate the third law of thermodynamics for finite $p$. However, the free energy recovers the result of the static approximation in the limit $p ınfty$. Therefore, in the infinite-$p$ limit, the static approximation becomes valid and our phase diagram is expected to be exact.

@incollection{statphys23_0162, abstract = {We study the $p$-spin interacting spin glass in a transverse field in the large-$p$ limit. Our purpose is to investigate three competing effects; quenched disorder, ferromagnetic bias, and quantum fluctuations. Although this model has already been studied by some researchers, we have extended their results and succeeded in clarifying some new properties. By using the Trotter decomposition, this quantum system is reduced to a corresponding classical system. The replica method is applied to the classical system and the equations of state are derived by the saddle-point method. Due to quantum effects, order parameters become dependent on time (Trotter index) and the equations are highly complex. We avoid the problem by employing the static approximation and analytically obtain the free energy and order parameters in the limit $p \rightarrow \infty$. The resultant phase diagram consists of four phases; the classical and quantum paramagnetic, ferromagnetic, and spin glass phases. In addition, we examine the validity of the static approximation by the large-$p$ expansion taking into account the time-dependent corrections in the ferromagnetic phase. In the classical paramagnetic and spin glass phases, it is known that the static approximation is valid and order parameters do not depend on times as long as $p$ is sufficiently large. For the ferromagnetic phase, our calculations show similar results to that of the two phases. Meanwhile, in the quantum paramagnetic phase, it is known that an order parameter is time-dependent and thermodynamic quantities violate the third law of thermodynamics for finite $p$. However, the free energy recovers the result of the static approximation in the limit $p \rightarrow \infty$. Therefore, in the infinite-$p$ limit, the static approximation becomes valid and our phase diagram is expected to be exact.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Obuchi, T. and Nishimori, H. and Sherrington, D.}, biburl = {https://www.bibsonomy.org/bibtex/2679c10754c3b0065873569513c1b6aa4/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {2116639cc0e2ec11d6706778d49397a8}, intrahash = {679c10754c3b0065873569513c1b6aa4}, keywords = {diagram effects glass interaction phase quantum spin statphys23 topic-9}, month = {9-13 July}, timestamp = {2007-06-20T10:16:13.000+0200}, title = {Phase diagram of the $p$-spin-interacting spin glass with ferromagnetic bias and a transverse field in the infinite-$p$ limit}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=162}, year = 2007 }