Davide De Gregorio’s research while affiliated with University of Messina and other places

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Publications (1)

The pentakis dodecahedron has 12 icosahedral vertices (red dots) and 20 dodecahedral vertices (yellow dots). There are five distinct ways to choose eight yellow dots forming a cube—then, the other 12 dodecahedral vertices are said to form a “co-cube”. The short edges of the PD mesh are colored in grey and the long edges in blue. The couplings entering the model Hamiltonian (1) are indicated.
Zero-temperature phase diagram of the lattice gas on a PD mesh. The phase boundaries are reported in the main text.
Lattice gas on a PD mesh, for γ=1/2 and T*=0.1,0.2,…,0.5. Top left: number of particles. Top right: reduced energy. Bottom left: icosahedral OP. Bottom right: dodecahedral OP. For the lowest temperatures, MC data refer to two distinct sequences of runs where μ* is respectively increased or decreased in steps of 0.1 (T*=0.1, blue and cyan dots; T*=0.2, emerald and green; T*=0.3, red and pink; T*=0.4, brown; and T*=0.5, black). For all temperatures but the lowest one, MC data are reported as lines. Hysteresis is evident for T*=0.1 and barely visible already for T*=0.2.
Lattice gas on a PD mesh, for γ=1/2 and T*=0.1,0.2,…,0.5. Top: reduced compressibility. Bottom left: Constant-μ specific heat. Bottom right: Constant-N specific heat. Symbols and notation as in Figure 3.
Lattice gas on a PD mesh, for γ=1 and T*=0.05: N vs. μ across the transition between ICO+CUB and ICO+COC. We plot data from two sequences of runs, ascending (blue) and descending (cyan). The top left and top right panels differ for the number of equilibrium cycles performed in each run, which is 5×106 and 5×107, respectively. Bottom panels: OPs for ICO+CUB and ICO+COC, for the simulation with 5×107 equilibrium cycles per run. We see a narrow interval of μ* values around 9/2 where the order is neither ICO+CUB nor ICO+COC.

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Classical and Quantum Gases on a Semiregular Mesh
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October 2021

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3 Citations

Davide De Gregorio

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The main objective of a statistical mechanical calculation is drawing the phase diagram of a many-body system. In this respect, discrete systems offer the clear advantage over continuum systems of an easier enumeration of microstates, though at the cost of added abstraction. With this in mind, we examine a system of particles living on the vertices of the (biscribed) pentakis dodecahedron, using different couplings for first and second neighbor particles to induce a competition between icosahedral and dodecahedral orders. After working out the phases of the model at zero temperature, we carry out Metropolis Monte Carlo simulations at finite temperature, highlighting the existence of smooth transitions between distinct “phases”. The sharpest of these crossovers are characterized by hysteretic behavior near zero temperature, which reveals a bottleneck issue for Metropolis dynamics in state space. Next, we introduce the quantum (Bose-Hubbard) counterpart of the previous model and calculate its phase diagram at zero and finite temperatures using the decoupling approximation. We thus uncover, in addition to Mott insulating “solids”, also the existence of supersolid “phases” which progressively shrink as the system is heated up. We argue that a quantum system of the kind described here can be realized with programmable holographic optical tweezers.

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Citations (1)

... To avoid having to be concernedwith boundary effects, a natural choice is a (two-dimensional) system of particles confined on a surface with the topology of a sphere. A further simplification is obtained by discretizing the space, e.g., by taking particles to lie at the nodes/sites of a dense, quasi-regular triangular mesh on the sphere [1]. The combination of a lower dimensionality and discrete particle positions can make the model amenable to an exact treatment, either analytic or numerical. ...

Reference:

Self-Assembly of Particles on a Curved Mesh
Classical and Quantum Gases on a Semiregular Mesh
Davide De Gregorio

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