This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-5250U CPU at 1.60GHz.
There were 512 solutions found in 2.804 seconds with 10 variables.
The unknowns stand for the values (in [0,1]) of a distribution function of a field created by a mixture of a ferro-antiferro-magnetic bond at some some points.
i1 : katsura(10,QQ)
2 2 2
o1 = {a + 2b + 2c + 2d + 2e + 2f + 2g + 2h + 2i + 2j - 1, a + 2b + 2c +
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2 2 2 2 2 2 2
2d + 2e + 2f + 2g + 2h + 2i + 2j - a, 2a*b + 2b*c + 2c*d + 2d*e +
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2
2e*f + 2f*g + 2g*h + 2h*i + 2i*j - b, b + 2a*c + 2b*d + 2c*e + 2d*f +
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2e*g + 2f*h + 2g*i + 2h*j - c, 2b*c + 2a*d + 2b*e + 2c*f + 2d*g + 2e*h +
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2
2f*i + 2g*j - d, c + 2b*d + 2a*e + 2b*f + 2c*g + 2d*h + 2e*i + 2f*j -
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2
e, 2c*d + 2b*e + 2a*f + 2b*g + 2c*h + 2d*i + 2e*j - f, d + 2c*e + 2b*f
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+ 2a*g + 2b*h + 2c*i + 2d*j - g, 2d*e + 2c*f + 2b*g + 2a*h + 2b*i + 2c*j
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2
- h, e + 2d*f + 2c*g + 2b*h + 2a*i + 2b*j - i}
o1 : List
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The object katsura is a method function.