Thermodynamic Fluctuations in Magnetic Phase Transition: Invar as a Prototype

We propose a first-principles formulism for system with spin fluctuations and apply it to the ordered Fe3Pt to uncover the Invar anomalies, including negative thermal expansion and spontaneous magnetization. The theory has coherently predicted the finite temperature intermixing between the fully ferromagnetic configuration and the spin-flipping configurations. We also discover a tri-critical point at which a high-temperature second-order phase transition, between the fully ferromagnetic configuration and the spin-flipping configurations, becomes first-order at low temperatures.