We give results from an accurate determination of the partition function of the three-dimensional Ising model on lattices of size up to 10 3 . We compute the two complex zeros of Z closest to the real temperature axis. From a finite-size-scaling analysis of these, we get the estimates v =0.6295 (10) for the correlation-length exponent and 0 = 52.2(7) for the angle between the first two zeros and the real u =e ~4 /3 axis.PACS numbers: 75.10.Hk, 75.40.CxWe have recently developed 1 " 3 a new technique that directly measures the partition function of a statisticalmechanical system by numerical methods. In the present paper, we give results for some critical properties of the three-dimensional Ising model by accurately measuring its partition function on cubic lattices (with periodic boundary conditions) of size up to 10 3 using our method. The details of our numerical simulation and analysis will be published elsewhere. 4 Here we will describe our method, give results for the two zeros closest to the critical point in the u =e ~4& plane and, from these, determine the correlation-length exponent v and the angle 0 between the first two zeros and the real u =e ~4P axis.The energy of a lattice configuration is Uj)Here the sum is over all nearest-neighbor pairs of lattice sites. E is integer valued, ranging from zero for the ordered state to a number of the order of the volume for the maximally frustrated state. The partition function iswhere P(E) is the number of states of the system at energy £", u =e ~4 fi , and E m =dL d /2. To make our simulation fast, we found it useful to update several independent lattices simultaneously. Our method to compute Z went as follows: We divided up the range of E values into sets containing four consecutive energies each. The last E value of one set was the first of the next set. Consider one of the sets. To initialize a lattice into that energy set, it was started in a disordered or ordered configuration and randomly chosen spins were flipped, the flip being accepted if the energy went in the desired direction. The independent lattices to be processed together were initialized independently.Once all the lattices were initialized, they were updated by flipping spins at sites chosen randomly (but the same site on all the lattices in a single trial flip). If the spin flip kept a lattice within the range of allowed energy values, it was accepted. These spin-flip attempts were repeated a large number of times, and the number of times the lattice energy had a given E value was recorded. This experiment was repeated over all sets. The relative probability for the system to be in one (E) or the other (£") energy state in the set is an unbiased estimator of the relative number of states P(E)/P(E') at these energy values. From the overlap in E between sets, one gets the complete partition function, apart from an irrelevant normalization factor.The choice of four energy values in a set is to allow the system to reach any local spin configuration from any other. One could have picked more than fo...

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