stata哈肯模型代码

以下是一个简单的 Stata 实现哈肯模型的代码：

* 定义哈肯模型的参数
scalar num_spins = 20
scalar num_trials = 1000
matrix J = J0
vector h = runiform(num_spins, -1, 1)

* 定义计算能量的函数
capture program drop calculate_energy
program calculate_energy, rclass
    syntax spins(anyarray)
    tempname energy
    local i 1
    local j 1
    scalar `energy' = 0
    forval i = 1/`num_spins' {
        forval j = 1/`num_spins' {
            scalar `energy' = `energy' + J[`i', `j'] * `spins'[`i'] * `spins'[`j']
        }
        scalar `energy' = `energy' + h[`i'] * `spins'[`i']
    }
    return scalar `energy'
end

* 定义模拟退火算法
capture program drop simulated_annealing
program simulated_annealing, rclass
    tempname spins
    matrix `spins' = runiform(1, `num_spins', 0, 1) > 0.5
    scalar t = 1.0
    scalar t_min = 0.00001
    scalar alpha = 0.9
    scalar delta_e = 0
    scalar e0 = calculate_energy(`spins')
    scalar e1 = 0
    scalar prob = 0
    scalar u = 0
    scalar i = 0
    scalar j = 0
    while t > t_min {
        forval i = 1/`num_trials' {
            scalar j = floor(runiform(1) * `num_spins') + 1
            scalar delta_e = 2 * h[`j'] * (`spins'[`j'] == 0) - 2 * h[`j'] * (`spins'[`j'] == 1)
            forval k = 1/`num_spins' {
                scalar delta_e = `delta_e' + 2 * J[`j', `k'] * `spins'[`j'] * `spins'[`k'] * (`spins'[`j'] == 0) - 2 * J[`j', `k'] * `spins'[`j'] * `spins'[`k'] * (`spins'[`j'] == 1)
            }
            if `delta_e' < 0 {
                scalar `spins'[`j'] = 1 - `spins'[`j']
            }
            else {
                scalar prob = exp(-`delta_e' / t)
                scalar u = runiform(1)
                if `prob' > `u' {
                    scalar `spins'[`j'] = 1 - `spins'[`j']
                }
            }
        }
        scalar t = `t' * `alpha'
    }
    return scalar(`spins'), calculate_energy(`spins')
end

* 定义初始自旋之间的相互作用矩阵 J0
matrix J0 = J
forval i = 1/`num_spins' {
    forval j = 1/`num_spins' {
        if `i' < `j' {
            scalar J0[`i', `j'] = 2 * runiform(1) - 1
            scalar J0[`j', `i'] = `J0'[`i', `j']
        }
    }
}

* 运行模拟退火算法
simulate `spins', `energy' = (simulated_annealing)
matrix list `spins'
scalar list `energy'

在这个代码中，我们首先定义了哈肯模型的参数，包括自旋数、尝试翻转自旋的次数、自旋之间的相互作用和外部磁场。然后我们定义了一个计算能量的函数 `calculate_energy()`，以及一个模拟退火算法 `simulated_annealing()`。在模拟退火算法中，我们首先随机初始化自旋状态，然后按照一定的温度和退火率进行退火过程，最终得到自旋状态和对应的能量。

由于 Stata 没有现成的矩阵加法和乘法运算符，我们需要使用循环来计算每个自旋之间的相互作用。在代码中，我们使用了一个初始自旋之间的相互作用矩阵 `J0`，并在初始化后使用循环来确保它是对称的。