Mean-Field Critical Behavior for the Contact Process |
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Authors: | Akira Sakai |
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Institution: | (1) Department of Applied Physics, Tokyo Institute of Technology, Tokyo, Japan;(2) Present address: Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada |
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Abstract: | The contact process is a model of spread of an infectious disease. Combining with the result of ref. 1, we prove that the critical exponents take on the mean-field values for sufficiently high dimensional nearest-neighbor models and for sufficiently spread-out models with d>4: ( )![ap](/content/u01231k5367137v7/xxlarge8776.gif) –
c as ![lambda](/content/u01231k5367137v7/xxlarge955.gif) ![darr](/content/u01231k5367137v7/xxlarge8595.gif)
c and ( ) (
c– )–1 as ![lambda](/content/u01231k5367137v7/xxlarge955.gif) ![uarr](/content/u01231k5367137v7/xxlarge8593.gif)
c, where ( ) and ( ) are the spread probability and the susceptibility of the infection respectively, and
c is the critical infection rate. Our results imply that the upper critical dimension for the contact process is at most 4. |
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Keywords: | contact process percolation critical exponents triangle condition mean-field behavior lace expansion |
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