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from scipy import optimize as opt import numpy as np from scipy.optimize import minimize import matplotlib.pyplot as plt from scipy.integrate import quad cb = 223.6 cf = 14.8 pi = np.pi m_h = 125.5 m_w = 80.4 m_z = 91.2 m_t = 178 v = 246.22 M = 600 mw2 = lambda phi: (m_w**2)*(phi**2/v**2) mz2 = lambda phi: (m_z**2)*(phi**2/v**2) mt2 = lambda phi: (m_t**2)*(phi**2/v**2) def jb(y_t): return quad((lambda x: x**2 * (np.log(1-np.exp(-np.sqrt(x**2+y_t**2))))), 0, np.infty)[0] def jf(z_t): return quad((lambda x: x**2 * (np.log(1+np.exp(-np.sqrt(x**2+z_t**2))))), 0, np.infty)[0] def V(phi, T, M): A = -m_h**2/4*v + 3*v**4/8*M**2 lbd = m_h**2/8*v**2 - 3/8*M**2 V0 = ((A*phi**2) + (lbd)*phi**4 + (1/8*M**2)*phi**6) MASSA_W = ((mw2(phi)**2)*np.log(mw2(phi)/m_w**2)) - ((3*mw2(phi)**2)/2) + (2 * mw2(phi))*(m_w**2) - (m_w**4)/2 MASSA_Z = ((mz2(phi)**2)*np.log(mz2(phi)/m_z**2)) - ((3*mz2(phi)**2)/2) + (2*mz2(phi))*(m_z**2) - (m_z**4)/2 MASSA_t = ((mt2(phi)**2)*np.log(mt2(phi)/m_t**2)) - ((3*mt2(phi)**2)/2) + (2*mt2(phi))*(m_t**2) - (m_t**4)/2 V1 = (1/(64*(pi**2)))*(MASSA_W+MASSA_Z+MASSA_t) if T != 0: del_V1 = ((T**4/(2*pi**2))*((6*jb(np.sqrt(mw2(phi))/T) + (3*jb(np.sqrt(mz2(phi))/T)) - (12*jf(np.sqrt(mt2(phi))/T))))) return V0+V1+del_V1 else: return V0+V1 def v_linha(phi, T): return V(phi, T, M)-V(1e-15, T, M) def find_tc(low, high): def vmin(T): phimin = minimize(lambda phi: v_linha(phi, T), v).x return v_linha(phimin, T) return opt.bisect(vmin, low, high) plt.figure(num=0, dpi=120.0) philist = np.arange(1e-15, 80, .1) plt.plot(philist, list(map(lambda x: v_linha(x, 153.5), philist))) plt.xlabel('$\phi$') plt.ylabel('V($\phi$,T)') plt.title('Potencial Efetivo') plt.grid(True)