The paper introduces a new global optimization method called *Simulated Tempering* (ST), which is designed to effectively simulate systems with a rough free energy landscape at finite non-zero temperatures. Unlike simulated annealing, where the temperature is a static variable that drives the system out of equilibrium, ST allows the temperature to be a dynamic variable while keeping the system in equilibrium. This method is particularly useful for systems with multiple coexisting states, such as the Random Field Ising Model (RFIM). The authors define a large configuration space that includes both the original variables \(X\) and a new variable \(m\). The probability distribution \(P(X, m)\) is chosen to be proportional to \(e^{-H(X, m)}\), where \(H(X, m)\) includes a term \(\beta_m H(X)\) and a constant \(g_m\). The \(\beta_m\) values are dynamically adjusted, allowing the system to explore different regions of the configuration space more efficiently. In the RFIM, the method significantly improves the simulation results compared to conventional Metropolis and cluster methods. The ST method helps decorrelate the system faster, allowing it to tunnel between different states more easily. The authors demonstrate that the ST method reduces correlation times for observable quantities by a factor of 6 compared to the Metropolis and cluster methods. They also show that the method provides more accurate estimates of the magnetization, even in cases where the Metropolis method gets trapped in a single state. The paper includes detailed analyses and results for the RFIM, showing that the ST method performs well across a range of temperatures and β values. The authors conclude that ST is a viable and efficient scheme for minimizing free energy in systems with complex free energy landscapes.The paper introduces a new global optimization method called *Simulated Tempering* (ST), which is designed to effectively simulate systems with a rough free energy landscape at finite non-zero temperatures. Unlike simulated annealing, where the temperature is a static variable that drives the system out of equilibrium, ST allows the temperature to be a dynamic variable while keeping the system in equilibrium. This method is particularly useful for systems with multiple coexisting states, such as the Random Field Ising Model (RFIM). The authors define a large configuration space that includes both the original variables \(X\) and a new variable \(m\). The probability distribution \(P(X, m)\) is chosen to be proportional to \(e^{-H(X, m)}\), where \(H(X, m)\) includes a term \(\beta_m H(X)\) and a constant \(g_m\). The \(\beta_m\) values are dynamically adjusted, allowing the system to explore different regions of the configuration space more efficiently. In the RFIM, the method significantly improves the simulation results compared to conventional Metropolis and cluster methods. The ST method helps decorrelate the system faster, allowing it to tunnel between different states more easily. The authors demonstrate that the ST method reduces correlation times for observable quantities by a factor of 6 compared to the Metropolis and cluster methods. They also show that the method provides more accurate estimates of the magnetization, even in cases where the Metropolis method gets trapped in a single state. The paper includes detailed analyses and results for the RFIM, showing that the ST method performs well across a range of temperatures and β values. The authors conclude that ST is a viable and efficient scheme for minimizing free energy in systems with complex free energy landscapes.