Importance of electron-lattice couplings have been recognized for long time in low-dimensional correlated systems like organic conductors. It, however, remains an unsolved problem to consider strong competition between different phases induced by changing dimensionality of the system. In order to approach this problem, I have recently developed a novel algorithm to deal with correlated systems coupled to lattice degrees of freedom based on the stochastic series expansion(SSE) method. By applying it to the spin-Peierls model with interchain exchange interaction, I discuss competition effects between antiferromagnetism and spin-Peierls transition. I also mention other applications of the present algorithm.
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