發(fā)布時(shí)間：2018-06-23 23:23

  本文選題：Ising模型 + 有限尺度標(biāo)度理論��； 參考：《物理學(xué)報(bào)》2017年19期

【摘要】：公共物品博弈是研究群體相互作用的經(jīng)典模型,廣泛用于解釋自私個(gè)體間合作的涌現(xiàn)和保持.本文從理論分析和蒙特卡羅模擬兩個(gè)方面研究了二維正方格子上一個(gè)有償懲罰機(jī)制下隨自我質(zhì)疑更新規(guī)則演化的公共物品博弈模型的相變特性.理論分析方面,將公共物品博弈模型轉(zhuǎn)化為一個(gè)外場(chǎng)不為零的鐵磁Ising模型.通過(guò)有效能量發(fā)現(xiàn):不存在懲罰時(shí),個(gè)體間的耦合強(qiáng)度為零,體系只有外場(chǎng)作用;存在懲罰時(shí),個(gè)體間包含最近鄰、次近鄰和第三近鄰相互作用且外場(chǎng)不為零.蒙特卡羅模擬方面,首先驗(yàn)證了理論分析的正確性,然后對(duì)公共物品博弈模型相關(guān)的一級(jí)相變和二級(jí)相變進(jìn)行了有限尺度標(biāo)度分析.研究發(fā)現(xiàn):1)蒙特卡羅模擬所得結(jié)果與類(lèi)Ising模型分析結(jié)果完全吻合;2)相比二維Ising模型,公共物品博弈的二級(jí)相變臨界指數(shù)發(fā)生了變化;3)公共物品博弈的一級(jí)相變與二維Ising模型相同.
[Abstract]:Public goods game is a classical model to study group interaction, which is widely used to explain the emergence and maintenance of selfish individual cooperation. In this paper, the phase transition characteristics of the game model of public goods evolving with the rules of self-challenge renewal under a paid punishment mechanism on a two-dimensional square lattice are studied from two aspects of theoretical analysis and Monte Carlo simulation. In theoretical analysis, the game model of public goods is transformed into a ferromagnetic Ising model with non-zero external field. It is found by effective energy that the coupling strength between individuals is zero when there is no punishment, and the system only has the external field action, and when there is punishment, the interaction between individuals includes the nearest neighbor, the second nearest neighbor and the third nearest neighbor, and the external field is not zero. In Monte Carlo simulation, the correctness of the theoretical analysis is first verified, and then the first-order and second-order phase transitions related to the game model of public goods are analyzed on a finite scale. It is found that the results obtained from Monte Carlo simulation are in good agreement with those of Ising-like model, and the results of two-dimension Ising model are in good agreement with those of two-dimension Ising model. The second order critical exponent of public goods game has changed 3) the first order phase transition of public goods game is the same as that of two dimensional Ising model.
【作者單位】： 昆明理工大學(xué)數(shù)據(jù)科學(xué)研究中心;昆明理工大學(xué)理學(xué)院;中國(guó)科學(xué)院理論物理研究所理論物理前沿重點(diǎn)實(shí)驗(yàn)室;中國(guó)科學(xué)院大學(xué)物理科學(xué)學(xué)院;
【基金】：昆明理工大學(xué)引進(jìn)人才科研啟動(dòng)基金項(xiàng)目(批準(zhǔn)號(hào):KKSY201607047) 國(guó)家自然科學(xué)基金(批準(zhǔn)號(hào):61573173)資助的課題~~
【分類(lèi)號(hào)】：O469
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本文編號(hào)：2058882