A quantum system can undergo a continuous phase transition at the absolute zero of temperature as some parameter entering its Hamiltonian is varied. These transitions are particularly interesting for, in contrast to their classical finite temperature counterparts, their dynamic and static critical behaviors are intimately intertwined. We show that considerable insight is gained by considering t...

whereM is a real, symmetric, positive-definite matrix (i.e. all eigenvalues are positive). This identity can be easily established by changing variables of integration to a basis in which M is diagonal. We will use this identity to compute the free energy density F , defined by Z = exp(−V F ) where V is the volume of spacetime. In the paramagnetic phase, r > 0, the perturbative expansion for F ...

The most spectacular consequence of interactions among particles is the appearance of new phases of matter whose collective behavior bears little resemblance to that of a few particles. How do the particles then transform from one macroscopic state to a completely different one. From a formal perspective, all macroscopic properties can be deduced from the free energy or the partition function. ...

Solid polymorphism in five compounds of the type [Me(H20)6](BF4)2 , where Me = Mn, Fe, Co, Ni and Zn, have been studied in the temperature range 120 330 K by DSC. For each substance at least three solid modifications have been found. In addition, for compounds with Me = Mn, Fe and Zn some new low temperature phase transitions have been observed. The transition temperatures for the [Me(H20)6](BF...

U nderstanding matter—a collection of many interacting constituents, such as atoms and electrons—is a major endeavor in physics. While most studies in this field have focused on matter that is in thermal equilibrium with its environment, many phenomena occurring in nature involve matter out of equilibrium. The reason for this disparity may lie in the often-repeated observation that, to paraphra...

In this lecture at a school for condensed matter physicists, I begin with basic concepts and tools for investigating phase transitions in quantum field theory. The very different roles of global and gauge symmetries in phase transitions will be elucidated. Among the important applications of the basic theory the thermodynamics of the electroweak transition is treated in detail, and the implicat...

The nonlocal nature of quantum entanglement has remained a subject of great interest since the earliest days of quantum mechanics as it causes many of the paradoxes and lies at the heart of the profound difference between quantum mechanics and classical physics. Quantum entanglement is observed primarily for simple quantum objects (photons or/and atoms) in environments specially designed to min...

region πa2 (26,50) πa1 (13,98) Figure 7 – Phase Transition curves in (L,m) and (N,L) plane with the useful area for abstraction Ideally, if a ground problem lies in the mushy region and has solution, then a useful abstraction operator shall map it into an abstract problem lying in the YES region. On the contrary, if a ground problem lies in the mushy region and has no solutions, then a useful a...