Phase transitions in systems of self-propelled agents and related network models

An important characteristic of flocks of birds, schools of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence. We address this issue by analyzing two representative network models closely related to systems of self-propelled particles. We present analytical as well as numerical results showing that the nature of the phase transition depends crucially on the way in which noise is introduced into the system.     

Photoinduced structural phase transitions in low-dimensional systems: Theoretical framework in charge-density-wave models

A theoretical framework for photoinduced structural transitions (PSPTs) is described with low-dimensional charge-density-wave (CDW) systems as typical examples. Our point of view is based on the concept of domain formation, which is expected to have the structure of a hetero-phase sandwiched between two domain walls. Common to all the cases here, we assume that the initial states are stable or metastable with an appreciable energy barrier so that a thermal phase transition cannot occur. Contrary to such stationarity in the ground states, there are various possibilities in photo-excited states, depending on system conditions. In this article, we focus on one of the most basic conditions, namely, the dimensionality or the geometry of the system and survey the expected features. Based on such a basic consideration, we review the work on MX-chains, which are typical quasi-one-dimensional materials. Since their two ground states in the half-filling case are identical except for a phase difference, the “photoinduced structural transition” in those systems are considered as a soliton-pair formation in the analogy of polyacetylene or mathematical models as φ⁴- and Sine-Gordon models. Next, we mention other CDW systems. Although they are rather theoretical, they convey two important concepts in cooperative PSPT: nonlinearity in the converted fraction as a function of the absorbed photon density, and aggregation of excitations.     

Quantum phase transitions in mesoscopic systems

Quantum phase transitions in mesoscopic systems are studied. It is shown that the main features of phase transitions, defined for infinite number of particles, N--> infinity, persist even for moderate N approximately 10. A Landau analysis of first order transitions is done and a "critical" exponent at the spinodal point is defined. Two order parameters are introduced to distinguish first from second order transitions. Applications to atomic nuclei, molecules, atomic clusters, and finite polymers are mentioned. Experimental evidence in atomic nuclei is presented.     

Quantum phase transitions in electronic systems

Quantum phase transitions occur at zero temperature when some non‐thermal control‐parameter like pressure or chemical composition is changed. They are driven by quantum rather than thermal fluctuations. In this review we first give a pedagogical introduction to quantum phase transitions and quantum critical behavior emphasizing similarities with and differences to classical thermal phase transitions. We then illustrate the general concepts by discussing a few examples of quantum phase transitions occurring in electronic systems. The ferromagnetic transition of itinerant electrons shows a very rich behavior since the magnetization couples to additional electronic soft modes which generates an effective long‐range interaction between the spin fluctuations. We then consider the influence of rare regions on quantum phase transitions in systems with quenched disorder, taking the antiferromagnetic transitions of itinerant electrons as a primary example. Finally we discuss some aspects of the metal‐insulator transition in the presence of quenched disorder and interactions.     

Tricritical phase transitions in semi-infinite systems

Semi-infinite systems with a bulk tricritical point are studied using a free energy functional of the Ginzburg-Landau-Wilson type. Tricritical surface exponents, order parameter profiles and the phase diagram are presented within mean field theory. In the case of ordinary and special transition, renormalization-group methods are used to obtain the exponents of a system withO(n)-symmetry to first order in ?=3?d and logarithmic corrections ind=3.