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In the present paper, we study a system of doped antiferromagnet in threedimensions at finite temperatures by using the t-J model, a canonical model ofstrongly-correlated electrons. We employ the slave-fermion representation ofelectrons in which an electron is described as a composite of a chargedspinless holon and a chargeless spinon. We introduce two kinds of U(1) gaugefields on links as auxiliary fields, one describing resonating valence bonds ofantiferromagnetic nearest-neighbor spin pairs and the other fornearest-neighbor hopping amplitudes of holons and spinons in the ferromagneticchannel. In order to perform numerical study of the system, we integrate outthe fermionic holon field by using the hopping expansion in powers of thehopping amplitude, which is legitimate for the region in and near theinsulating phase. The resultant effective model is described in terms ofbosonic spinons and the two U(1) gauge fields, and a collective field for holepairs. We study this model by means of Monte-Carlo simulations, calculating thespecific heat, spin correlation functions, and instanton densities. We obtain aphase diagram in the hole concentration-temperature plane, which is in goodagreement with that observed recently for clean and homogeneous underdopedsamples.

Antiferromagnetic, metal-insulator, and superconducting phase transitions in underdoped cuprates: Slave-fermion t-J model in the hopping expansion