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arXiv 1701.06164cond-mat.stat-mech
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两个恒温器之间的Glauber Ising链

Glauber's Ising chain between two thermostats

F. Cornu, H. J. Hilhorst

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43 pages
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摘要：

我们考虑一个一维伊辛模型，其中每个$N$自旋与两个不同温度的恒温器$T_1$和$T_2$接触。在Glauber动力学下，在有效中间温度$T(T_1,T_2)$，定态恰好与平衡态重合。然而，该系统在恒温器之间携带非平凡的能量电流。利用费米子化技术，对初始处于平衡态的链在任意温度$T_0$下，计算了在有限时间间隔$τ$内，时间积分能流${\cal Q}$的概率$P({\cal Q};τ)$的傅里叶变换.在长的时间限制，我们确定相应的生成函数的累积量每网站和单位时间$\langle{\cal Q}^n\rangle_{\rm c}/(Nτ)$，并明确给出那些与$n=1,2,3,4.$我们表现出各种现象在特定的制度：动力学平均场效应时，一个恒温器翻转任何自旋往往比其他的，以及耗散对恒温器在零温度。此外，当系统大小$N$变为无穷大而有效温度$T$为零时，每单位时间的${\cal Q}$的累积量随$N$线性增长，并且等于随机游走过程的累积量。在两个适当的标度制度，涉及$T$和$N$，我们表现出的第一个修正的自旋-自旋相关长度$ξ(T)$的比例和大小$N$的依赖性。

英文摘要：

We consider a one-dimensional Ising model each of whose $N$ spins is in contact with two thermostats of distinct temperatures $T_1$ and $T_2$. Under Glauber dynamics the stationary state happens to coincide with the equilibrium state at an effective intermediate temperature $T(T_1,T_2)$. The system nevertheless carries a nontrivial energy current between the thermostats. By means of the fermionization technique, for a chain initially in equilibrium at an arbitrary temperature $T_0$ we calculate the Fourier transform of the probability $P({\cal Q};τ)$ for the time-integrated energy current ${\cal Q}$ during a finite time interval $τ$. In the long time limit we determine the corresponding generating function for the cumulants per site and unit of time $\langle{\cal Q}^n\rangle_{\rm c}/(Nτ)$ and explicitly give those with $n=1,2,3,4.$ We exhibit various phenomena in specific regimes: kinetic mean-field effects when one thermostat flips any spin less often than the other one, as well as dissipation towards a thermostat at zero temperature. Moreover, when the system size $N$ goes to infinity while the effective temperature $T$ vanishes, the cumulants of ${\cal Q}$ per unit of time grow linearly with $N$ and are equal to those of a random walk process. In two adequate scaling regimes involving $T$ and $N$ we exhibit the dependence of the first correction upon the ratio of the spin-spin correlation length $ξ(T)$ and the size $N$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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