\#1 \#1\#2\#3

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**Critical Exponents of the Classical**

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**3D Heisenberg Model:**

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**A Single-Cluster Monte Carlo Study**

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$^1$ and [*Wolfhard Janke*]{}$^2$

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$^1$ [Institut für Theoretische Physik, Freie Universität Berlin]{}

[Arnimallee 14, D-1000 Berlin 33, Germany]{}

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$^2$ [Höchstleistungsrechenzentrum, Forschungszentrum Jülich]{}

[Postfach 1913, D-5170 Jülich, Germany ]{}

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Introduction
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Critical exponents are the distinguishing parameters characterizing continuous phase transitions. Most theoretical estimates of their values have been calculated along three different routes. First, assuming universality, from (resummed) perturbation expansions of generic field theoretical models. Second, from high-temperature series expansions of lattice models, and third, from Monte Carlo (MC) simulations of the associated Boltzmann distributions. All these approaches are based on resummation or extrapolation techniques whose systematic errors are difficult to control. To gain confidence in the numerical values of the exponents it is therefore quite important to have several independent approaches for cross-checks available.

Until a few years ago the precision of Monte Carlo estimates was comparatively poor, since this approach was plagued not only by systematic but also by statistical errors. The problem is that MC algorithms based on [*local*]{} update procedures are severely hampered near criticality by extremely long autocorrelation times (so-called critical slowing down) 