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We propose a new implementation of the replica-exchange method (REM) in whichreplicas follow a pre-planned route in temperature space instead of a randomwalk. Our method satisfies the detailed balance condition in the proposedroute. The method forces tunneling events between the highest and lowesttemperatures to happen with an almost constant period. The number of tunnelingcounts is proportional to that of the random-walk REM multiplied by the squareroot of moving distance in temperature space. We applied this newimplementation to two kinds of REM and compared the results with those of theconventional random-walk REM. The test system was a two-dimensional Isingmodel, and our new method reproduced the results of the conventionalrandom-walk REM and improved the tunneling counts by three times or more thanthat of the random-walk REM.

Designed-walk replica-exchange method for simulations of complex systems