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Register a new userHexatic phase in the two-dimensional Gaussian-core model
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We present a Monte Carlo simulation study of the phase behavior of two-dimensional classical particles repelling each other through an isotropic Gaussian potential. As in the analogous three-dimensional case, a reentrant-melting transition occurs upon compression for not too high temperatures, along with a spectrum of water-like anomalies in the fluid phase. However, in two dimensions melting is a continuous two-stage transition, with an intermediate hexatic phase which becomes increasingly more definite as pressure grows. All available evidence supports the Kosterlitz-Thouless-Halperin-Nelson-Young scenario for this melting transition. We expect that such a phenomenology can be checked in confined monolayers of charge-stabilized colloids with a softened core.
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We trace with unprecedented numerical accuracy the phase diagram of the Gaussian-core model, a classical system of point particles interacting via a Gaussian-shaped, purely repulsive potential. This model, which provides a reliable qualitative description of the thermal behavior of interpenetrable globular polymers, is known to exhibit a polymorphic FCC-BCC transition at low densities and reentrant melting at high densities. Extensive Monte Carlo simulations, carried out in conjunction with accurate calculations of the solid free energies, lead to a thermodynamic scenario that is partially modified with respect to previous knowledge. In particular, we find that: i) the fluid-BCC-FCC triple-point temperature is about one third of the maximum freezing temperature; ii) upon isothermal compression, the model exhibits a fluid-BCC-FCC-BCC-fluid sequence of phases in a narrow range of temperatures just above the triple point. We discuss these results in relation to the behavior of star-polymer solutions and of other softly repulsive systems.
We investigate the two-dimensional melting of biological tissues that are modeled by deformable polymeric particles with multi-body interactions described by the Voronoi model. We identify the existence of the intermediate hexatic phase in this system, and the critical scaling of the associated solid-hexatic phase transition with the critical exponent $ uapprox0.65$ for the divergence of the correlation length. Moreover, we clarify the discontinuous nature of the hexatic-liquid phase transition in this system. These findings are achieved by directly analyzing systems spatial configurations with two generic machine learning approaches developed in this work, dubbed scanning-probe via which the possible existence of intermediate phases can be efficiently detected, and information-concealing via which the critical scaling of the correlation length in the vicinity of generic continuous phase transition can be extracted. Our work provides new physical insights into the fundamental nature of the two-dimensional melting of biological tissues, and establishes a new type of generic toolbox to investigate fundamental properties of phase transitions in various complex systems.
Two-dimensional crystals of classical particles are very peculiar in that melting may occur in two steps, in a continuous fashion, via an intermediate hexatic fluid phase exhibiting quasi-long-range orientational order. On the other hand, three-dimensional spheres repelling each other through a fast-decaying bounded potential of generalized-exponential shape (GEM4 potential) can undergo freezing into cluster crystals, allowing for more that one particle per lattice site. We hereby study the combined effect of low spatial dimensionality and extreme potential softness, by investigating the phase behavior of the two-dimensional (2D) GEM4 system. Using a combination of density-functional theory and numerical free-energy calculations, we show that the 2D GEM4 system displays one ordinary and several cluster triangular-crystal phases, and that only the ordinary crystal first melts into a hexatic phase. Upon heating, the difference between the various cluster crystals fades away, eventually leaving a single undifferentiated cluster phase with a pressure-modulated site occupancy.
Spontaneous onset of a low temperature topologically ordered phase in a 2-dimensional (2D) lattice model of uniaxial liquid crystal (LC) was debated extensively pointing to a suspected underlying mechanism affecting the RG flow near the topological fixed point. A recent MC study clarified that a prior crossover leads to a transition to nematic phase. The crossover was interpreted as due to the onset of a perturbing relevant scaling field originating from the extra spin degree of freedom. As a counter example and in support of this hypothesis, we now consider V-shaped bent-core molecules with rigid rod-like segments connected at an assigned angle. The two segments of the molecule interact with the segments of all the nearest neighbours on a square lattice, prescribed by a biquadratic interaction. We compute equilibrium averages of different observables with Monte Carlo techniques as a function of temperature and sample size. For the chosen molecular bend angle and symmetric inter-segment interaction between neighbouirng molecules, the 2D system shows two transitions as a function of T: the higher one at T1 leads to a topological ordering of defects associated with the major molecular axis without a crossover, imparting uniaxial symmetry to the medium described by the first fundamental group of the order parameter space $pi_{1}$= $Z_{2}$ (inversion symmetry). The second at T2 leads to a medium displaying biaxial symmetry with $pi_{1}$ = Q (quaternion group). The biaxial phase shows a self-similar microscopic structure with the three axes showing power law correlations with vanishing exponents as the temperature decreases.
The presence of stable topological defects in a two-dimensional (textit{d} = 2) liquid crystal model allowing molecular reorientations in three dimensions (textit{n} = 3) was largely believed to induce defect-mediated Berzenskii-Kosterlitz-Thouless (BKT) type transition to a low temperature phase with quasi long-range order. However, earlier Monte Carlo (MC) simulations could not establish certain essential signatures of the transition, suggesting further investigations. We study this model by computing its equilibrium properties through MC simulations, based on the determination of the density of states of the system. Our results show that, on cooling, the high temperature disordered phase deviates from its initial progression towards the topological transition, crossing over to a new fixed point, condensing into a nematic phase with exponential correlations of its director fluctuations. The thermally induced topological kinetic processes continue, however limited to the length scales set by the nematic director fluctuations, and lead to a second topological transition at a lower temperature. We argue that in the (textit{d} = 2, textit{n} = 3) system with a biquadratic Hamiltonian, the presence of additional molecular degree of freedom and local $Z_{2}$ symmetry associated with lattice sites, together promote the onset of an additional relevant scaling field at matching length scales in the high temperature region, leading to a crossover.
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