The 4th Edition of Cengel & Boles Thermodynamics:An Engineering Approach takes thermodynamics education to the next level through its intuitive and innovative approach. A longtime favorite among students and instructors alike because of its highly engaging, studentoriented conversational writing style, this book is now the to most widely adopted thermodynamics text in theU.S. and in the world.
{"title":"Thermodynamics","authors":"J. Luscombe","doi":"10.1201/9781003139669-1","DOIUrl":"https://doi.org/10.1201/9781003139669-1","url":null,"abstract":"The 4th Edition of Cengel & Boles Thermodynamics:An Engineering Approach takes thermodynamics education to the next level through its intuitive and innovative approach. A longtime favorite among students and instructors alike because of its highly engaging, studentoriented conversational writing style, this book is now the to most widely adopted thermodynamics text in theU.S. and in the world.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74936514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Scaling theories and the renormalization group","authors":"J. Luscombe","doi":"10.1201/9781003139669-8","DOIUrl":"https://doi.org/10.1201/9781003139669-8","url":null,"abstract":"","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77129096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-14DOI: 10.1103/PhysRevB.103.174404
P. Lajk'o, F. Igl'oi
The antiferromagnetic quantum Ising chain has a quantum critical point which belongs to the universality class of the transverse Ising model (TIM). When a longitudinal field ($h$) is switched on, the phase transition is preserved, which turns to first-order for $h/Gamma to infty$, $Gamma$ being the strength of the transverse field. Here we will re-examine the critical properties along the phase transition line. During a quantum block renormalization group calculation, the TIM fixed point for $h/Gamma>0$ is found to be unstable. Using DMRG techniques, we calculated the entanglement entropy and the spin-spin correlation function, both of which signaled a divergent correlation length at the transition point with the TIM exponents. At the same time, the bulk correlation function has a jump and the end-to-end correlation function has a discontinuous derivative at the transition point. Consequently for finite $h/Gamma$ the transition is of mixed-order.
反铁磁量子Ising链具有一个量子临界点，该临界点属于横向Ising模型(TIM)的普适性类。当纵向场($h$)打开时，相变保持不变，在$h/Gamma to infty$变为一阶，$Gamma$为横向场的强度。在这里，我们将重新考察沿相变线的关键性质。在量子块重整化群计算中，发现$h/Gamma>0$的TIM不动点是不稳定的。利用DMRG技术，我们计算了纠缠熵和自旋-自旋相关函数，两者都表明了与TIM指数在过渡点处的发散相关长度。同时，体相关函数有一个跃变，端到端相关函数在过渡点处有一个不连续导数。因此，对于有限$h/Gamma$，跃迁是混合阶的。
{"title":"Mixed-order transition in the antiferromagnetic quantum Ising chain in a field","authors":"P. Lajk'o, F. Igl'oi","doi":"10.1103/PhysRevB.103.174404","DOIUrl":"https://doi.org/10.1103/PhysRevB.103.174404","url":null,"abstract":"The antiferromagnetic quantum Ising chain has a quantum critical point which belongs to the universality class of the transverse Ising model (TIM). When a longitudinal field ($h$) is switched on, the phase transition is preserved, which turns to first-order for $h/Gamma to infty$, $Gamma$ being the strength of the transverse field. Here we will re-examine the critical properties along the phase transition line. During a quantum block renormalization group calculation, the TIM fixed point for $h/Gamma>0$ is found to be unstable. Using DMRG techniques, we calculated the entanglement entropy and the spin-spin correlation function, both of which signaled a divergent correlation length at the transition point with the TIM exponents. At the same time, the bulk correlation function has a jump and the end-to-end correlation function has a discontinuous derivative at the transition point. Consequently for finite $h/Gamma$ the transition is of mixed-order.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80751769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-11DOI: 10.1103/PHYSREVRESEARCH.3.023064
Jaron Kent-Dobias, J. Kurchan
We study the saddle-points of the $p$-spin model -- the best understood example of a `complex' (rugged) landscape -- when its $N$ variables are complex. These points are the solutions to a system of $N$ random equations of degree $p-1$. We solve for $overline{mathcal N}$, the number of solutions averaged over randomness in the $Ntoinfty$ limit. We find that it saturates the B'ezout bound $logoverline{mathcal N}~Nlog(p-1)$. The Hessian of each saddle is given by a random matrix of the form $C^dagger C$, where $C$ is a complex symmetric Gaussian matrix with a shift to its diagonal. Its spectrum has a transition where a gap develops that generalizes the notion of `threshold level' well-known in the real problem. The results from the real problem are recovered in the limit of real parameters. In this case, only the square-root of the total number of solutions are real. In terms of the complex energy, the solutions are divided into sectors where the saddles have different topological properties.
{"title":"Complex complex landscapes","authors":"Jaron Kent-Dobias, J. Kurchan","doi":"10.1103/PHYSREVRESEARCH.3.023064","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.3.023064","url":null,"abstract":"We study the saddle-points of the $p$-spin model -- the best understood example of a `complex' (rugged) landscape -- when its $N$ variables are complex. These points are the solutions to a system of $N$ random equations of degree $p-1$. We solve for $overline{mathcal N}$, the number of solutions averaged over randomness in the $Ntoinfty$ limit. We find that it saturates the B'ezout bound $logoverline{mathcal N}~Nlog(p-1)$. The Hessian of each saddle is given by a random matrix of the form $C^dagger C$, where $C$ is a complex symmetric Gaussian matrix with a shift to its diagonal. Its spectrum has a transition where a gap develops that generalizes the notion of `threshold level' well-known in the real problem. The results from the real problem are recovered in the limit of real parameters. In this case, only the square-root of the total number of solutions are real. In terms of the complex energy, the solutions are divided into sectors where the saddles have different topological properties.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88347779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-11DOI: 10.21468/SciPostPhys.10.5.116
G. Perfetto, B. Doyon
We derive an exact formula for the scaled cumulant generating function of the time-integrated current associated to an arbitrary ballistically transported conserved charge. Our results rely on the Euler-scale description of interacting, many-body, integrable models out of equilibrium given by the generalized hydrodynamics, and on the large deviation theory. Crucially, our findings extend previous studies by accounting for inhomogeneous and dynamical initial states in interacting systems. We present exact expressions for the first three cumulants of the time-integrated current. Considering the non-interacting limit of our general expression for the scaled cumulant generating function, we further show that for the partitioning protocol initial state our result coincides with previous results of the literature. Given the universality of the generalized hydrodynamics, the expression obtained for the scaled cumulant generating function is applicable to any interacting integrable model obeying the hydrodynamic equations, both classical and quantum.
{"title":"Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems","authors":"G. Perfetto, B. Doyon","doi":"10.21468/SciPostPhys.10.5.116","DOIUrl":"https://doi.org/10.21468/SciPostPhys.10.5.116","url":null,"abstract":"We derive an exact formula for the scaled cumulant generating function of the time-integrated current associated to an arbitrary ballistically transported conserved charge. Our results rely on the Euler-scale description of interacting, many-body, integrable models out of equilibrium given by the generalized hydrodynamics, and on the large deviation theory. Crucially, our findings extend previous studies by accounting for inhomogeneous and dynamical initial states in interacting systems. We present exact expressions for the first three cumulants of the time-integrated current. Considering the non-interacting limit of our general expression for the scaled cumulant generating function, we further show that for the partitioning protocol initial state our result coincides with previous results of the literature. Given the universality of the generalized hydrodynamics, the expression obtained for the scaled cumulant generating function is applicable to any interacting integrable model obeying the hydrodynamic equations, both classical and quantum.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82469840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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