Abstract The last‐passage (LP) Monte Carlo algorithms for the charge density on an L‐shaped conducting surface are further developed by deriving a quadrupole LP Green's function on the L‐shaped flat surface. To demonstrate the algorithm, charge densities on an L‐shaped conductor are computed in 3D space and it is found that these results agree very well with the ones from the Given‐Hwang's original last‐passage algorithm on a flat surface. Compared with the Given‐Hwang's LP algorithm, the quadrupole LP one is very suitable for charge density near the L‐shaped edge boundary.
Cooperation in an open dynamic system fundamentally depends upon information distributed across its components. Yet in an environment with rapidly evolving complexity, this information may need to change adaptively to enable cooperative interactions. Combining the methods of evolutionary game theory, agent-based simulation, and statistical physics, we develop a model of the evolution of cooperation in an ageing population of artificial decision makers playing spatial tag-mediated prisoner’s dilemma games with their ingroup neighbors and with genetically unrelated immigrant agents. We introduce the concept of time-varying tags such that the phenotypic features of ‘new’ agents can change into ‘approved’ following variable approval times. In the standard 4-strategy model with fixed tags, we identified a critical cost [Formula: see text] above which cooperation transitioned abruptly into the phase of pure defection. In our generalized 6-strategy model with time-varying tags, the maintenance of elevated cooperation was observed for a much wider region of the parameter space, peaking at intermediate approval times and cost values above [Formula: see text]. Our findings reveal the existence of optimal approval times leading to high levels of cooperation if a fraction of the population adopts the strategy with an egalitarian generosity directed towards both native and approved agents, regardless of their actual origin.
It is well established that transport properties of colossal magnetoresistive manganites can be qualitatively explained by the small polaron model incorporating the double-exchange interaction. We have improved this model by taking into account effects of phonon frequency hardening below ${T}_{c}.$ It is found that the effects are significant in that the resistivity drop for $T<{T}_{c}$ becomes much steeper and the magnetoresistance is enhanced substantially at ${T}_{c}$ in accord with experiments. This model is applied to understand the evolution of ${T}_{c}$ with the chemical pressure in ${R}_{0.7}{A}_{0.3}{\mathrm{MnO}}_{3}$ series.
Cooperation in an open dynamic system fundamentally depends upon information distributed across its components. Yet in an environment with rapidly enlarging complexity, this information may need to change adaptively to enable not only cooperation but also the mere survival of an organism. Combining the methods of evolutionary game theory, agent-based simulation, and statistical physics, we develop a model of the evolution of cooperation in an ageing population of artificial decision makers playing spatial tag-mediated prisoner's dilemma games with their ingroup neighbors and with genetically unrelated immigrant agents. In our model with six strategies we introduce the concept of time-varying tags such that the phenotypic features of 'new' agents can change into 'approved' following variable approval times. Our Monte Carlo simulations show that ingroup-biased ethnocentric cooperation can dominate only at low costs and short approval times. In the standard 4-strategy model with fixed tags, we identified a critical cost $c_{\mathrm{crit}}$ above which cooperation transitioned abruptly into the phase of pure defection, revealing remarkable fragility of ingroup-biased generosity. In our generalized 6-strategy model with time-varying tags, elevated cooperation was observed for a wider region of the parameter space, peaking at intermediate approval times and cost values above $c_{\mathrm{crit}}$. Our findings show that in an open system subject to immigration dynamics, high levels of social cooperation are possible if a fraction of the population adopts the strategy with an egalitarian generosity directed towards both native and approved naturalized citizens, regardless of their actual origin. These findings also suggest that instead of relying upon arbitrarily fixed approval times, there is an optimal duration of the naturalization procedure from which the society as a whole can profit most.
Alloy disorder can affect ferromagnetism and metal-insulator transitions of correlated lattice fermion systems in subtle and often unexpected ways.Solving the Hubbard model and the periodic Anderson model within dynamical mean-field theory we show that alloy disorder can increase the Curie temperature of a non-disordered system, and also yields novel Mott or Kondo insulators at fractional electronic densities.
Abstract The last‐passage (LP) Monte Carlo algorithm for the charge density on a flat conducting surface held at a constant potential is further developed by deriving a generalized last‐passage Green's function on the flat surface. In the previous research, a centered Green's function on the flat surface was used. In the new last‐passage algorithm, an off‐centered point on the flat surface inside the Green's function hemisphere can also be used. To demonstrate the algorithm, the charge density on a circular disk is calculated and it is found that the result agrees very well with the analytic solution. Compared with the previous centered LP, the generalized algorithm is better in most cases and has an advantage that it can use the same potential distribution over the LP hemisphere for different locations inside of the lower flat surface including the center of the hemisphere for the charge density.
Abstract We study the thermodynamic and dynamic phase transitions (TPT and DPT) of the spin- 1/2 and spin-1 Ising models on three graphs constructed on the Sierpiński carpet. This study employs Monte Carlo methods, specifically the Wolff and Metropolis algorithms, in conjunction with finite-size scaling analysis. By calculating the critical temperature and critical exponent ratio γ/ν associated with the TPT, we demonstrate that the three graphs exhibit an identical critical exponent ratio for both the spin- 1/2 and spin-1 Ising models within statistical error. Furthermore, we explore the kinetic Ising model by varying the period of the oscillating external magnetic field and verify the existence of the DPT. We find that the critical exponent ratio γ/ν for the DPT matches that of the TPT. Our results suggest that the critical exponents or their ratios for continuous phase transitions in equilibrium and non-equilibrium systems with short-range interactions are independent of the graph structure and interaction type, as long as the background space is the same.
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